Question

Finding the Equation of a Parabola Find an equation of the parabola whose graph is shown.

Short answer

The equation of parabola for the graph is :$x^2=8y$

Step-by-step solution

Step 1. Given information.

The graph of parabola

Step 2. The equation of the parabola for the graph.

On studying the graph, the parabola opens upwards andp>0, the coordinates of focus are obtained.

On substituting the value of p in the equation $x^2=4py$to obtain an equation of a parabola $y^2=4px$

The graph for the parabola is –

The focus has the coordinate (0,2), sop=2.

Now, substituting the value of p in equation $x^2=4py$, we get the equation as :

$\begin{array}{l}{x}^2=4\left(2\right)y\\ \Rightarrow x^2=8y.\end{array}$