Question

Find the equation of the parabola that passes through the point (0,11) and has its vertex at (3, -7)

Answer 1

Given:

Given that the points

`(x,y)=(0,11)`

And vertex

`(h,k)=(3,-7)`

Required:

To find the equation of the parabola.

Step-by-step explanation:

The equation of parabola in vertex form is

`y=a(x-h)^2+k`

Therefore,

`y=a(x-3)^2-7`

Now we have to find a, by using the points.

`\begin{gathered} 11=a(0-3)^2-7 \\ \\ 11=9a-7 \\ \\ 11+7=9a \\ \\ 9a=18 \\ \\ a=(18)/(9) \\ \\ a=2 \end{gathered}`

So,

`y=2(x-3)^2-7`

Final Answer:

`y=2(x-3)^2-7`