Question

Write an equation for each parabola.

Short answer

The equation of the parabola is$x^2=4\left(y-1\right)$.

Step-by-step solution

Step 1. Given information .

Consider the given graph and the points located on it .

Step 2.  Formula used .

The formula used to find the equation of parabola is ${\left(x-h\right)}^2=4a\left(y-k\right)$.

where h , k are the points of vertex$\left(h,k\right)=\left(0,1\right)$and focus$\left(x,y\right)=\left(2,2\right)$.

Step 3.  Find the equation of the parabola .

Substitute the value of $\left(h,k\right)=\left(0,1\right)$and $\left(x,y\right)=\left(2,2\right)$in the equation of parabola .

localid="1646929727056" $$\begin{gathered} {\left(x-h\right)}^2=4a\left(y-k\right) \\ {\left(2-0\right)}^2=4a\left(2-1\right) \\ a=1 \end{gathered}$$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646930160222" $$\begin{gathered} \left(x-h^2\right)=4a\left(y-k\right) \\ {\left(x-0\right)}^2=4\times 1\left(y-1\right) \\ {x}^2=4\left(y-1\right) \end{gathered}$$