Answer:
(2,-9)
Step-by-step explanation:
Set the quadratic equal to zero.
[tex]y = {x}^{2} - 4x - 5[/tex]
Factor
[tex](x - 5)(x + 1)[/tex]
Set each of these factors to zero
[tex]x - 5 = 0[/tex]
and
[tex]x + 1 = 0[/tex]
[tex]x = 5[/tex]
and
[tex]x = - 1[/tex]
Plot the midpoint of the two values.
[tex]( \frac{5 + ( - 1)}{2} ) = 2[/tex]
So the middle term is 2 and the other terms are 5 and -1.
Now the vertex is
[tex]2 {}^{2} - 4(2) - 5 = - 9[/tex]
So the vertex is
(2,-9)
