The vertex of the prabola whose equation is
[tex]f(x)=ax^2+bx+c[/tex]is (h, k), where
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=f(h) \end{gathered}[/tex]The vertex is minimum if a has positive value
The vertex is maximum if a has negative value
Since the given equation is
[tex]f(x)=-4x^2+24x+3[/tex]a = -4
b = 24
c = 3
Let us find h
[tex]\begin{gathered} h=\frac{-24}{2(-4)} \\ h=\frac{-24}{-8} \\ h=3 \end{gathered}[/tex]Let us use h to find k
[tex]\begin{gathered} k=f(h)=f(3) \\ k=-4(3)^2+24(3)+3 \\ k=-36+72+3 \\ k=39 \end{gathered}[/tex]The vertex of the parabola is (3, 39)
Since a = -4
That means a is negative, then
The vertex is maximum