Question

The quadratic function f(x)= ax2 + 8x + c has a vertex at (1,9). What are the values of a and c?

Answer 1

we get that the x coordinate of the vertex is

$\frac{-8}{2a}=1\rightarrow2a=-8\rightarrow a=-\frac{8}{2}=-4$

and if we replace 1 in the function we get 9. So

$\begin{gathered} -4\cdot1+8\cdot1+c=9\rightarrow-4+8+c=9 \\ 4+c=9\rightarrow c=9-4=5 \end{gathered}$

so we get that a=-4 and c=5