Question

I am having trouble understanding how to find the equation of a parabola. I have the vertex and the focus. The vertex is (-2,5) and the focus is (-2,6). Can you explain in an easy to understand way how to do this kind of problem?

Answer 1

Given:

The vertex is (-2,5).

`(h,k)=(-2,5)`

And the focus is (-2,6).

Required:

To find the equation of the parabola.

Step-by-step explanation:

The equation of a parabola in vertex form is

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

Here,

`(h,k)=(-2,5)`

Therefore,

`\begin{gathered} y=a(x-(-2))^2+5 \\ \\ y=a(x+2)^2+5 \end{gathered}`

And given that focus is

`(h,k+(1)/(4)a)=(-2,6)`
`\begin{gathered} k+(1)/(4)a=6 \\ \\ 5+(1)/(4)a=6 \\ \\ (1)/(4)a=6-5 \\ \\ (1)/(4)a=1 \\ \\ a=4 \end{gathered}`

Therefore, the equation of parabola is,

`y=4(x+2)^2+5`

Final Answer:

The equation of parabola is,

`y=4(x+2)^(2)+5`