Answer :
[tex]V=(1,-11)[/tex]
1) Considering that the Vertex form of a quadratic equation is given by the following formula:
[tex]y=a(x-h)^2+k[/tex]2) We can rewrite that into the Vertex formula noticing that in m(x)=4x²-8x-7, we can find out the vertex by using the Vertex formula for the x-coordinate:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{8}{2(4)}=1 \end{gathered}[/tex]Now let's plug "1" into the function to get the k value, k is the y-coordinate of the vertex:
[tex]\begin{gathered} m(1)=4(1)^2-8(1)-7 \\ m(1)=4-8-7 \\ m(1)=-11 \end{gathered}[/tex]Notice that since we plugged x=1, then we get the corresponding y-value for that in this case y=-11 and the y-coordinate is the vertex y-coordinate (k)
3) So we can write out the vertex formula of m(x) =4x²-8x-7. Let's pick the vertex formula and plug into that the coefficient "a" and the values for "h" and "k"
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=4(x-1)^2-11 \\ m(x)=4(x-1)^2-11 \end{gathered}[/tex]Note that into this equation m(x) and y are the same thing.