Question

Write an equation for each parabola.

Short answer

The equation of parabola is$y^2=x-1$.$y^2=x-1$.

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 and x , y are the points of focus .

Step 3.  Find the equation of parabola .

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

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

Further simplify .

Substitute the value of a in the equation of parabola .

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