2024 Vertex form to standard form calculator

While the standard quadratic form is a x 2 + b x + c = y, the vertex form of a quadratic equation is y = a ( x − h) 2 + k. In both forms, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up ( + a) or down ( − a ). (I think about it as if the parabola was a bowl of applesauce .... Walmart hermitage pa

Convert each quadratic from Vertex Form to Standard Form. Then solve the quadratic equations. 11) y = 2(x − 2)2 − 2 0 2 4 6 8 −2 2 4 6 12) y = ... Jun 23, 2010 ... Completing the square for vertex form | Quadratic equations | Algebra I | Khan Academy. Fundraiser. 744K views · 13 years ago # ...The standard form for a quadratics function (as a polynomial function) is f (x) = ax2 + bx +c. The standard for for the equation of a parabola (also called the vertex form) is like the standard form for other conic sections. (If the parabola opens sideways, it includes the points (h +a,k ± 1) and has form x = a(y −k)2 +h .)Free Function Transformation Calculator - describe function transformation to the parent function step-by-step For standard form (y = ax 2 + bx + c): h = -b/2a. k = c - b 2 /(4a) (Alternatively, you can convert standard form into vertex form to identify the values.) For vertex form (y = a*(x …Given one of the forms of a quadratic function, convert to the other two forms. Problem 1 : y = x 2 − 6x − 7 (i) Vertex form (ii) Factored form. Solution : (i) Converting into vertex form : y = x 2 − 6x − 7. Coefficient of x 2 is 1. So, don't have to factories anything. Write the coefficient of x as multiple of 2. y = x 2 − 2 ⋅x ⋅ ...The standard form calculator instantly converts a number into its standard form. Enter a number and the calculator will help you write it as a multiple of decimal and a power of 10. Working of Our Standard Form Calculator: The standard notation calculator provides you with super fast conversion of an integer to standard notations.Sep 10, 2021 · Contents [ hide] 1 Quadratic equation of parabola: Vertex to Standard form. 1.1 From vertex to standard form conversion: 1.1.1 Step 1: Simplify the binomial by multiplying by itself. 1.1.2 Step 2: Simplify the other numbers. The resultant equation is the standard form. 1.2 Example (1): 1.3 Example (2):You just need to enter the parabola equation in the specified input fields and hit on the calculator button to acquire vertex, x intercept, y intercept, focus, axis of symmetry, and directrix as output. ... The standard form of the equation is y = ax 2 + bx + c. So, a = 5, b = 4, c = 10. The parabola equation in vertex form is y = a(x-h) 2 + k ...We want to put it into vertex form: y=a(x-h) 2 +k; We can convert to vertex form by completing the square on the right hand side; 36 is the value for 'c' that we found to make the right hand side a perfect square trinomial; Our perfect square trinomial factors into two identical binomials, (x+6)•(x+6) The vertex of an equation in vertex form ...Free Ellipse calculator - Calculate ellipse area, center, radius, foci, vertice and eccentricity step-by-step. The vertex form calculator converts standard form to vertex form and vertex form to the standard form & also gives step-by-step calculations along with a graph.Nov 1, 2023 · Answer: The standard to vertex form calculator is an online tool that converts quadratic equations from their standard form (ax^2 + bx + c = 0) to their vertex form (a(x - h)^2 + k = 0). It simplifies quadratic equations, reveals the vertex (minimum/maximum point), provides the axis of symmetry, enhances understanding of the parabola's behavior ... Use the information provided to write the vertex form equation of each parabola. 1) y= x2+ 16x+ 71. y= (x+ 8)2+ 7 2) y= x2− 2x− 5. y= (x− 1)2− 6 3) y= −x2− 14x− 59. y= −(x+ 7)2− 10 4) y= 2x2+ 36x+ 170. y= 2(x+ 9)2+ 8 5) y= x2− 12x+ 46. y= (x− 6)2+ 10 6) y= x2+ 4x y= (x+ 2)2− 4 7) y= x2− 6x+ 5. y= (x− 3)2− 4 8) y ... Feb 4, 2024 ... In this video we discuss how to write the vertex form of a parabola (quadratic) using the equation x=-b/2a as well as using completing the ...Completing the Square. Converts Standard form to Vertex form. Get the free "Completing the Square" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Nov 20, 2016 ... Converting Vertex Form to Standard Form. 11K views · 7 years ago ... How To Calculate The Perimeter of A Square And A Rectangle. Maths And ...A vertex form calculator is an online tool designed to make it super easy for you to figure out the vertex form (highest or lowest point) of a quadratic equation, which is essential in graphing and understanding the shape of a parabola curve.Apr 28, 2011 ... Use the method of Completing the Square to convert a quadratic function from standard form to vertex form.What you need to know about Standard Form of a Quadratic Function. The Quadratic Equation in Standard Form is. \. ax²+bx+c = 0 } Then, the Vertex (h,k) can be found from the above Standard Form using. \. h= {-b \over 2a} , k=f ( {-b \over 2a }) } Once computed, the vertex coordinates are plugged into the Vertex Form of a Parabola, see …the vertex of a quadratic is so named as it gives the vertex of a quadratic equation. Other features can be found easily from the equation in this form as well. 1 Feb 2, 2021 ... TI-84 Calculator Tutorial: Find the Vertex of a Quadratic Function. 829 ... How do you convert from standard form to vertex form of a quadratic.The formula for calculating eccentricity is e = c/a. In this formula, “e” refers to the eccentricity, “a” refers to the distance between the vertex and the center and “c” refers to...Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryFree Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b ± √(b^2 - 4ac)) / (2a) Does any quadratic equation have two solutions? There can be 0, 1 or 2 solutions to a quadratic equation.Fill it out as soon as possible, and be smart about how you do it. Going to college is all about filling out forms. Even before you get it, you have to fill out standardized tests,...Vertex Form Calculator. Vertex form calculator is an online tool that helps to find the vertex point of a quadratic equation graph. You can find vertices using both standard or vertex forms. The vertex form converter will calculate the y-intercept as well. You can also convert the standard form to vertex form through this calculator. vertex to standard form calculator: Let's explore the step-by-step procedure to convert a quadratic equation from vertex form to standard form. Step 1: Expand the Vertex Form. Begin by expanding the vertex form equation. Square the binomial $ (x - h) $ and multiply it by the coefficient $ a $: \[ f(x) = a(x - h)^2 + k \]The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b ± √(b^2 - 4ac)) / (2a) Does any quadratic equation have two solutions? There can be 0, 1 or 2 solutions to a quadratic equation.Send us Feedback. Free Parabola calculator - Calculate parabola foci, vertices, axis and directrix step-by-step. 2) the roots of the parabola can be found via the quadratic formula. So applying the arithmetic average formula (a+b)/2 where a is -b+sqrt (bsquared-4ac)/2a and b is -b-sqrt (bsquared-4ac)/a gives -b/2a as solution for x coordinate of vertex. This formula also works if the parabola has only one root. Oct 15, 2014 ... Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again! Join Our Geometry Teacher Community Today!Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System ... Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution. Physics. ... convert to vertex form. en ...The formula for calculating eccentricity is e = c/a. In this formula, “e” refers to the eccentricity, “a” refers to the distance between the vertex and the center and “c” refers to...To convert a quadratic equation from standard form to vertex form, you can follow these steps: Rewrite the equation in the form y = ax 2 + bx + c, where a, b, and c are the coefficients of the equation. Complete the square. Simplify the equation by combining like terms on both sides. Rewrite the equation in the form y = a (x-h) 2 + k, where (h ... Free functions vertex calculator - find function's vertex step-by-step ... Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal ... Form; Distance; Use this calculator to express a quadratic function in vertex form, showing all the steps and the formula. Learn how to find the vertex form, the standard form, and the x- and y-coordinates of the vertex. See examples and …FEEDBACK. Hyperbola calculator will help you to determine the center, eccentricity, focal parameter, major, and asymptote for given values in the hyperbola equation. Also, this tool can precisely finds the co vertices and conjugate of a function. In this context, you can understand how to find a hyperbola, it’s a graph and the standard form ...Jan 18, 2024 · Before we give some examples of writing numbers in standard form in physics or chemistry, let's recall from the above section the standard form math formula:. a = b × 10 n.. We said that the number b should be between 1 and 10.This means that, for example, 1.36 × 10⁷ or 9.81 × 10⁻²³ are in standard form, but 13.1 × 10¹² isn't because …Sep 27, 2023 ... Subscribe. Completing the Square - Solving Quadratic Equations │Algebra. Vertex to standard form #algebra #quadraticequations. 259. Dislike.A vertex form calculator is an online tool designed to make it super easy for you to figure out the vertex form (highest or lowest point) of a quadratic equation, which is essential in graphing and understanding the shape of a parabola curve.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Use our online Parabola calculator to find the vertex form and standard form. Enter the values for X and Y co-ordinates in this Standard equation of a parabola calculator and click on calculate to know the result. This Parabola equation solver calculator helps you to solve your academic equations and engineering algebraic problems with ease ...Jun 14, 2009 ... Converting a quadratic equation from Vertex Form to Standard Form involves FOIL. Each form of the quadratic tells you a little something ...The calculator generates standard form equations. General (standard form) Equation of a conic section ... is the vertex and x=h is the axis of symmetry or line of symmetry; Note: this is the representation of an upward facing …With a basic understanding of high school level algebra, you can convert the standard form to the vertex form. Start with the standard form of the parabolic equation; for example, y = (x + 3)² + 4. When plotted on a graph, the parabola will have a vertex of 3, 4. Expand the polynomial within the parentheses: (x+3) (x+3).Jan 18, 2024 · The slope-intercept and standard form are two methods of expressing an equation of a line in the two-dimensional plane.. The standard form of a linear equation is. Ax + By + C = 0. where A, B, and C are constants. Some methods of solving systems of linear equations assume that you have your equations in the standard form.. The slope …Apr 6, 2020 ... Comments15 ; A1 - Converting Factored Form to Vertex Form. Rademaker Math · 74K views ; A1 - Converting Standard Form to Factored Form. Rademaker ...The axis of symmetry calculator shows the complete steps involved in calculating the vertex that divides the parabola into two equal parts. Also, the tool shows a graph that better helps to understand the behavior of a symmetrical axis in a plane. ... Reduce the given expression into a standard quadratic function form such as: \(ax^{2} + b x ...ISO insurance forms are a standardized set of documents that are used in the insurance industry. They provide a uniform way for companies to collect and transmit information about ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Standard Form Equation of a Circle | DesmosAug 25, 2020 · Example. In geometry, a vertex form is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. For example, a square has four corners, each is called a vertex. The plural form of the vertex is vertices.Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step 1) Factor Quadratic Equations with Leading coefficient A = 1. We are to factor the Quadratic Equation. x 2 – 6x+8 . The 2 zeros when multiplied have to equal 8. That could be 8 and 1 OR 4 and 2, and their negatives. Additionally, they have to add to -6 which implies. the 2 zeros must be -4 and -2.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Nov 28, 2023 · The standard form of the quadratic equation can also be represented by f(x)=a(x-h)^2 +k where (h,k) is the vertex of a parabola. This is also known as the vertex form of a quadratic function. You can convert big or small numbers into standard forms using the online tool standard form calculator. A standard form of Quadratic EquationSend us Feedback. Free Parabola calculator - Calculate parabola foci, vertices, axis and directrix step-by-step. 9TH GRADE PRE ALGEBRA. least common multiple chart. Polymathlove.com includes good facts on turning vertex form to standard form calculator, grouping and the square and other math subjects. Just in case you need to have advice on arithmetic or matrix algebra, Polymathlove.com is without question the excellent place to go to!Step1: (Use Binomial Formula) y=a (x²-2hx+h²)+k y = a(x² − 2hx + h²) + k Step2: (Distribute and Combine the like terms ah² and k) y=ax²- (2ah)x+ (ah²+k) y = ax² − (2ah)x + (ah² + k) Vertex to Standard Form Calculator Video: How to Convert from Vertex Form to Standard Form of a Quadratic Equation How do you find the Vertex of a Quadratic Equation? This is the best quadratic equation program out there. It will do roots, the discriminant, vertex, graph it, show the table, roots to equation, standard to completed square form, focus, value/function of directrix, and length of the Latus Rectum. It will also handle imaginary numbers. tenchiquad83p.zip: 1k: 03-01-01: Quadratic SolverEquations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. vertex …Vertex Form Calculator Convert the formula of a parabola from standard to vertex form or vertex to standard form using the vertex formula calculator below. Convert Standard to Vertex Form Convert Vertex to …Step1: (Use Binomial Formula) y=a (x²-2hx+h²)+k y = a(x² − 2hx + h²) + k Step2: (Distribute and Combine the like terms ah² and k) y=ax²- (2ah)x+ (ah²+k) y = ax² − (2ah)x + (ah² + k) Vertex to Standard Form Calculator Video: How to Convert from Vertex Form to Standard Form of a Quadratic Equation How do you find the Vertex of a Quadratic Equation? Apr 6, 2020 ... Comments15 ; A1 - Converting Factored Form to Vertex Form. Rademaker Math · 74K views ; A1 - Converting Standard Form to Factored Form. Rademaker ...Free Polynomial Standard Form Calculator - Reorder the polynomial function in standard form step-by-step Use our online Parabola calculator to find the vertex form and standard form. Enter the values for X and Y co-ordinates in this Standard equation of a parabola calculator and click on calculate to know the result. This Parabola equation solver calculator helps you to solve your academic equations and engineering algebraic problems with ease ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. vertex …Jan 25, 2024 · Vertex Form To Standard Form Worksheet Answer Key 2020-2021 - Fill and Check Details Hw vertex form 2 .pdf. Form standard vertex worksheet quadratic functions 7a sse asse fif convert functionVertex quadratic equation definition Algebra i with mr. smith: deltamath assignmentConvert equation from vertex form to standard calculator …Vertex Form Calculator. Vertex form calculator is an online tool that helps to find the vertex point of a quadratic equation graph. You can find vertices using both standard or vertex forms. The vertex form converter will calculate the y-intercept as well. You can also convert the standard form to vertex form through this calculator.The straight-line depreciation formula is to divide the depreciable cost of the asset by the asset’s useful life. Accounting | How To Download our FREE Guide Your Privacy is import...To convert metric measurements to United States standard system measurements, you have two options. You can use mathematics and calculate the answer or use an online conversion too...Dec 8, 2018 ... It seems you are typo in this line equation = a (x + h) ** 2 + k . 'a' is not a function. May be a * (x+h) is what you are looking for.vertex form calculator. glencoe mathematics algebra 1 form 2. Students solve and graph quadratic equations by factoring. clep calculas. math worksheets- x and y intercepts. how to teach excel to 1st grade. converting decimals to fractions worksheets. solpass math/7th grade. formulas needed for gauss for gr7. Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System ... Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution. Physics. ... convert to vertex form. en ...vertex form calculator. glencoe mathematics algebra 1 form 2. Students solve and graph quadratic equations by factoring. clep calculas. math worksheets- x and y intercepts. how to teach excel to 1st grade. converting decimals to fractions worksheets. solpass math/7th grade. formulas needed for gauss for gr7. You can change a quadratic equation from standard form to vertex form by completing the square! This tutorial takes you through the process step-by-step. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long.First, compute the x-coordinate of the vertex. h = – b/2a = - (-6) / (2*3) = 1 . Next, compute the y-coordinate of the vertex by plugging h=1 into the given equation: k …The axis of symmetry calculator shows the complete steps involved in calculating the vertex that divides the parabola into two equal parts. Also, the tool shows a graph that better helps to understand the behavior of a symmetrical axis in a plane. ... Reduce the given expression into a standard quadratic function form such as: \(ax^{2} + b x ...Learn how to find the vertex of a parabola, the vertex form of a quadratic equation, and how to convert from standard to vertex form or vice versa. Use the …The two ways to solve a Quadratic Forms in Vertex Form. We can solve a Quadratic Forms in Vertex Form y = a (x-h)²+k in 2 ways. (a) We transform it into Standard Form to use the above Quadratic Formula again. Example: 2 (x+5/4)²-49/8=0 . We finally have 2x²+5x-3=0 . We again use the above Quadratic Formula to arrive at the 2 solutions …Nov 28, 2023 · The standard form of the quadratic equation can also be represented by f(x)=a(x-h)^2 +k where (h,k) is the vertex of a parabola. This is also known as the vertex form of a quadratic function. You can convert big or small numbers into standard forms using the online tool standard form calculator. A standard form of Quadratic EquationThe parabola calculator will instantly determine parabola-related parameters and displays the graph of the parabolic expressions. Choose What to Input: Standard Form: x = ay² + by + c. a. b. c. Calculate. 4/5 (52 Votes) Disclaimer: The results generated by the tool should be considered for educational purposes only.The vertex form of a quadratic equation is. a (x - h) 2 + k. where a is a constant that tells us whether the parabola opens upwards or downwards, and (h, k) is the location of the vertex of the parabola. This is something that we cannot immediately read from the standard form of a quadratic equation. Vertex form can be useful for solving ...

The vertex form of a quadratic equation is. a (x - h) 2 + k. where a is a constant that tells us whether the parabola opens upwards or downwards, and (h, k) is the location of the vertex of the parabola. This is something that we cannot immediately read from the standard form of a quadratic equation. Vertex form can be useful for solving .... Crock pots at amazon

Oct 21, 2023 · How to Convert a Number to Standard Form. Standard form of a number is a x 10 b where a is a number, 1 ≤ | a | < 10. b is the power of 10 required so that the standard form is mathematically equivalent to the original number. Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The vertex form to standard form calculator works by taking the input of the vertex form equation and using the standard algorithms to convert the equation into standard form. The calculator will then provide the standard form of the equation as output. This tool can save a considerable amount of time and effort, especially when working with ... To convert a quadratic equation from standard form to vertex form, you can follow these steps: Rewrite the equation in the form y = ax 2 + bx + c, where a, b, and c are the coefficients of the equation. Complete the square. Simplify the equation by combining like terms on both sides. Rewrite the equation in the form y = a (x-h) 2 + k, where (h ... The vertex is denoted P (h, k), where h is the x-coordinate and k is the y-coordinate. You can find the vertex given the standard form using the following formulas. h = -b 2a. k = c – b² 4a. Thus, h is equal to negative b divided by 2 times a, and k is equal to c minus b squared divided by 4 times a . Modern Real Estate Practice in Pennsylvania, 10th edition, PDF version. From vertex form to standard form calculator to solving linear equations, we have all the details included. Come to Solve-variable.com and read and learn about numbers, mixed numbers and plenty of additional math subject areas. Nov 13, 2023 · When written in "vertex form ":• (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0). • notice that the h value is subtracted in this form, and that the k value …The vertex form of a quadratic equation is written like f (x) = a(x – h)2 + k, with the letter h and the letter k being the vertex point of the parabola. It can be used to create a...Advertisement Once you determine that you're eligible for the foreign tax credit, the next question is: How much of a credit can you get? Typically, credit seekers are required to ...FEEDBACK. Hyperbola calculator will help you to determine the center, eccentricity, focal parameter, major, and asymptote for given values in the hyperbola equation. Also, this tool can precisely finds the co vertices and conjugate of a function. In this context, you can understand how to find a hyperbola, it’s a graph and the standard form ...Convert Standard to Vertex form. Step1: Enter your Quadratic Equation in Standard Form, Step2: Press SOLVE to find the Vertex Form. STEP BY STEP. ... Tip: When using the above Standard Form to Vertex Form Calculator to solve $$ 3x²-6x-2=0$$ we must enter the 3 coefficients a,b,c as $$ a=3, b=-6, c=-2 $$.free works sheets for grade 3. trinomial calculator. Right from Standard To Vertex Form Calculator to solving equations, we have got all the pieces included. Come to Polymathlove.com and discover division, square and several other algebra topics.Use the information provided to write the vertex form equation of each parabola. 1) y= x2+ 16x+ 71. y= (x+ 8)2+ 7 2) y= x2− 2x− 5. y= (x− 1)2− 6 3) y= −x2− 14x− 59. y= −(x+ 7)2− 10 4) y= 2x2+ 36x+ 170. y= 2(x+ 9)2+ 8 5) y= x2− 12x+ 46. y= (x− 6)2+ 10 6) y= x2+ 4x y= (x+ 2)2− 4 7) y= x2− 6x+ 5. y= (x− 3)2− 4 8) y ... A general vertex form is represented as: How to convert the standard form into vertex form? As mentioned before, you can convert the standard form into vertex form. A standard form is written as: Y = ax 2 +bx+c. You will have to: Make the coefficient of x 2, 1. Find the value to complete the square from the coefficient of x. Close the square ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Quadratic Function - Vertex Form | DesmosVertex to Standard Converter Description This program converts vertex form (Y-K=A*(X-H)^2) to standard (AX+B(X^2)+C) Author Joel Smith ([email protected]) Category TI-83/84 Plus BASIC Math Programs (Geometry) File Size 1,294 bytes File Date and Time Thu May 31 00:48:31 2001 Documentation Included? Yes Free functions and line calculator - analyze and graph line equations and functions step-by-stepOct 6, 2021 · Each endpoint of the major axis is the vertex of the ellipse (plural: vertices), and each endpoint of the minor axis is a co-vertex of the ellipse. The center of an ellipse is the midpoint of both the major and minor axes. ... STANDARD FORMS OF THE EQUATION OF AN ELLIPSE WITH CENTER $(0,0)$ The standard form of the equation of an ellipse …Free functions and line calculator - analyze and graph line equations and functions step-by-step.

Vertex form to standard form calculator - Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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