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$\left(x,y\right)=\left(2,0\right)$.

Step 3. Find the equation of parabola .

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

localid="1646930530938" $$\begin{gathered} {\left(x-h\right)}^2=4a\left(y-k\right) \\ {\left(2-0\right)}^2=4a\left(0+1\right) \\ a=1 \end{gathered}$$$$\begin{gathered} y=a{\left(x-h\right)}^2+k \\ 0=a{\left(2-0\right)}^2+\left(-1\right) \\ a=\frac{1}{4} \end{gathered}$$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646930607016" $$\begin{gathered} {\left(x-h\right)}^2=4a\left(y-k\right) \\ {\left(x-0\right)}^2=4\times 1\left(y+1\right) \\ {x}^2=4\left(y+1\right) \end{gathered}$$