Question

Need help with only #10. write the equation of each parabola in vertex form

Answer 1

The vertex form of the equation of a parabola is given to be:

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

where

`(h,k)\Rightarrow\text{ Vertex coordinates}`

The question provides the vertex coordinates to be:

`(h,k)=(7,4)`

Substituting this value into the vertex form equation, we get:

`y=a(x-7)^2+4`

We are given the coordinates of a point on the parabola to be:

`(x,y)=(5,16)`

We can use this point to get the value of a in the vertex formula by substituting into the equation:

`\begin{gathered} 16=a(5-7)+4 \\ 16-4=a(-2)^2 \\ 12=4a \\ a=(12)/(4) \\ a=3 \end{gathered}`

Therefore, the vertex form of the equation of the parabola is given to be:

`y=3\mleft(x-7\mright)^2+4`