Question

Write an equation for each parabola.

Short answer

The equation of the parabola is$y^2+2y+x-3=0$.

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 $\left(h,k\right)=\left(2,1\right)$and focus$\left(x,y\right)=\left(1,0\right)$.

Step 3. Find the equation of parabola .

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

localid="1646931030050" $$\begin{gathered} {\left(y-k\right)}^2=-4a\left(x-h\right) \\ {\left(0-1\right)}^2=-4a\left(1-2\right) \\ a=\frac{1}{4} \end{gathered}$$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646931164241" $$\begin{gathered} {\left(y-k\right)}^2=-4a\left(x-h\right) \\ {\left(y-1\right)}^2=-4\times \frac{1}{4}\left(x-2\right) \\ {y}^2+2y+x-3=0 \end{gathered}$$