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)

hello : A) (-5, - 34)

Step-by-step explanation:

f (x) = x2 + 10x - 9

= (x² + 10x + 25) - 25 - 9

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

answer : A) (-5, - 34)

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)