Convert y = (x+1) (x-9) to vertex form

y = (x - 4) ² - 25

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

y = (x + 1) (x - 9) ← expand factors using FOIL, thus

y = x² - 8x - 9

To complete the square

add/subtract (half the coefficient of the x - term) ² to x² - 8x

y = x² + 2 ( - 4) x + 16 - 16 - 9

= (x - 4) ² - 25 ← in vertex form