Question

Write an equation for the parabola.

Short answer

The equation of the parabola is$y^2-2y-x+1=0$.

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 center is $\left(h,k\right)$and focus is $\left(x,y\right)$.

Step 3. Find the equation of parabola .

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

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

Further simplify .

Substitute the value of a in the equation of parabola .

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