Question

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)

Answer 1

hello : A) (-5, -34)

Explanation:

f(x) = x2 + 10x - 9

= (x² +10x +25)-25 -9

f(x) = (x+5)² -34 standard vertex form

answer : A) (-5, -34)

Answer 2

A) (-5, -34)

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)