What is the vertex of the graph of f(x) = x2 + 10x - 9? a) (-5, -34) b) (-5, -9) c) (5, -9) d) (5, 66)

A) (-5, -34)

Step-by-step explanation:

f(x) = x^2 + 10x - 9

We complete the square to get the equation in vertex form

Take the coefficient of the x term and divide by 2 then square it.  We add it and then subtract it not to change the value of the equation

f(x) = x^2 + 10x +(10/2)^2 - (10/2)^2 - 9

f(x) = x^2 +10x +25 -25 -9

f(x) = (x^2 +10x +25) -34

The term in parentheses simplified to (x+10/2) ^2

     = (x+5)^2 -34

   = (x - -5)^2 -34

This is in the form (x-h)^2 +k

The vertex is (h,k)  h=-5 and k=-34

(-5,-34)

x = 3 ± √(5+y)