Question

Given the general formF(x)=a(x^2)+bx+cConvert it to vertex form also known as standard form by putting the values for a, h & k into the correct boxes.F(x)=a(x-h)^2+kIdentify the vertex(h,k)

Answer 1

Given the equation of the function:

`F(x)=4x^2+8x+(-7)`

We will make a complete square, to rewrite the given function as the general form F(x)=a(x-h)^2+k

So, the equation will be as follows:

`\begin{gathered} F(x)=4(x^2+2x)+(-7) \\ F(x)=4(x^2+2x+1-1)+(-7) \\ F(x)=4(x^2+2x+1)+4\cdot(-1)+(-7) \\ F(x)=4(x+1)^2+(-11) \\ F(x)=4(x-(-1))^2+(-11) \end{gathered}`

Compare the last equation with the general form

So,

`h=-1,k=-11`

So, the answer will be Vertex = (-1, -11)