Question

Write the quadratic function in the form (see equation) Then, give the vertex of its graph

Answer 1

The given function is

`g(x)=-3x^2+24x-45`

a = -3

b= 24

c = -45

`\begin{gathered} h=-(b)/(2a) \\ h=-(24)/(2(-3)) \\ h=-(24)/(-6) \\ h=4 \end{gathered}`

Substitute x by 4 to find k

`\begin{gathered} f(4)=-3(4)^2+24(4)-45 \\ f(4)=-48+96-45 \\ f(4)=3 \\ k=3 \end{gathered}`

The function is

`g(x)=-3(x-4)^2+3`

The vertex is (h, k) = (4, 3)