Vertical reflection: The function $y=x^2$ is reflected over the $x$-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: \displaystyle \begin{align} y &= f(3x)\\ &= \sin(3x) \end{align}. [7] How do I draw a graph with the function f(x) = -4x^2 + 32? As an example, let $f(x) = x^3$. Horizontal translation: The function $f(x)=x^2$ is translated both left and right by two.