We get the following information:
[tex]\frac{-b}{2a}=3\rightarrow-\frac{b}{a}=6\rightarrow b=-6a[/tex]
and
[tex]\begin{gathered} 9a+3b+c=-5 \\ 16a+4b+c=-2 \end{gathered}[/tex]
So if we replace b=-6a. We get
[tex]\begin{gathered} 9a+-18a+c=-5 \\ 16a-24a+c=-2 \\ \text{therefore} \\ -9a+c=-5 \\ -8a+c=-2 \\ \text{therefore} \\ 9a-c=5 \\ -8a+c=-2 \\ a=3 \\ \end{gathered}[/tex]
having a=3
we get that
[tex]\begin{gathered} b=-6\cdot3=-18 \\ \text{and} \\ 27-c=5 \\ c=22 \end{gathered}[/tex]
the equation is
[tex]f(x)=3x^2-18x+22[/tex]
