Question

Write an equation for each parabola.

Short answer

The equation of the parabola is $y^2=\frac{1}{2}x+1$.

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${\left(y-k\right)}^2=4a\left(x-h\right)$

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

Step 3.  Find the equation of parabola .

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

$$\begin{gathered} {\left(y-k\right)}^2=4a\left(x-h\right) \\ {\left(1-0\right)}^2=4a\left(0+2\right) \\ a=\frac{1}{8} \end{gathered}$$

Further simplify .

Substitute the value of a in the equation of parabola.

localid="1646928656388" $$\begin{gathered} {\left(y-k\right)}^2=4a\left(x-h\right) \\ {\left(y-0\right)}^2=4\times \frac{1}{8}\left(x+2\right) \\ {y}^2=\frac{1}{2}x+1 \end{gathered}$$