The zeros of the function are:
[tex]\begin{gathered} -(x+3)(x-7)=0 \\ x=-3 \\ or \\ x=7 \end{gathered}[/tex]The vertex is a point V(h,k) on the function. It's either at the base or the top of the function, depending upon wether it opens, upward or downward respectively.
For a function of the form:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{The vertex(extreme value) is:} \\ h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m(x)=-x^2+4x+21 \\ a=-1 \\ b=4 \\ c=21 \\ h=\frac{-4}{2(-1)}=\frac{-4}{-2}=2 \\ k=m(h)=-(2)^2+4(2)+21=-4+8+21=25 \end{gathered}[/tex]Hence, the extreme value is 25 at x = 2
That's it, do you have any question?
