Vertical reflection: The function [latex]y=x^2[/latex] is reflected over the [latex]x[/latex]-axis.

In this case, 100% of readers who voted found the article helpful, earning it our reader-approved status. You can shift a parabola based on its equation. Even a kid can understand. A translation moves every point by a fixed distance in the same direction.

September 2014 A transformation takes a basic function and changes it slightly with predetermined methods. March 2017 Thank you for, "Building a solar oven was easy with the geometric definition of the parabola. Which equation will produce the narrowest parabola when graphed.

As an example, consider again the initial sinusoidal function: If we want to induce horizontal shrinking, the new function becomes: [latex]\displaystyle \begin{align} y &= f(3x)\\ &= \sin(3x) \end{align}[/latex]. [7] How do I draw a graph with the function f(x) = -4x^2 + 32? As an example, let [latex]f(x) = x^3[/latex]. Horizontal translation: The function [latex]f(x)=x^2[/latex] is translated both left and right by two.

(adsbygoogle = window.adsbygoogle || []).push({}); Transformations alter a function while maintaining the original characteristics of that function.

In general, a vertical stretch is given by the equation y = bf (x) y = b f (x). A translation moves every point in a function a constant distance in a specified direction. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7e\/Graph-a-Parabola-Step-1-Version-2.jpg\/v4-460px-Graph-a-Parabola-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/7e\/Graph-a-Parabola-Step-1-Version-2.jpg\/aid4162801-v4-728px-Graph-a-Parabola-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

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If we want to vertically stretch the function by a factor of three, then the new function becomes: [latex]\displaystyle \begin{align} y &= 3f(x) \\ &= 3\sin(x) \end{align}[/latex].

One possible translation of [latex]f(x)[/latex] would be [latex]x^3 + 2[/latex]. A rotation is a transformation that is performed by “spinning” the object around a fixed point known as the center of rotation. Thanks to all authors for creating a page that has been read 166,475 times. September 2015 Calculate the reflection of a function over the [latex]x[/latex]-axis, [latex]y[/latex]-axis, or the line [latex]y=x[/latex]. To learn how to shift the graph of your parabola, read on! To make a table, simply choose a value for x, such as 0, and plug it into the original equation to solve for y.



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