Question

Write an equation for the parabola.

Short answer

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

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

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

Step 3. Find the equation of parabola .

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

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

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646931694920" $$\begin{gathered} {\left(x-h\right)}^2=-4a\left(y-k\right) \\ {\left(x-1\right)}^2=-4\times \frac{1}{4}\left(y-2\right) \\ {x}^2-2x+y-1=0 \end{gathered}$$