Question

What is an equation of a parabola with the given vertex and focus? Vertex: (-2,5); focus: (-2,6). Show all the steps that you used to solve this problem.

Answer 1

the equation of a parabola is;

`\begin{gathered} y=(1)/(4(f-k))(x-h)^2+k \\ \\ (h,k)\text{ = vertex} \\ \\ (h,f)\text{ = focus} \end{gathered}`

Given;

`\begin{gathered} (h,k)=(-2,5), \\ \\ (h,f)=(-2,6) \\ \\ h=-2,k=5,f=6 \end{gathered}`

Thus,

`\begin{gathered} y=(1)/(4(6-5))(x+2)^2+5 \\ \\ y=(1)/(4)(x+2)^2+5 \end{gathered}`

Thus, the equation of the parabola in vertex form is;

`y=(1)/(4)(x+2)^(2)+5`