Answer:
y = (x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Given
y = (x + 2)(x - 3) ← expand factors
= x² - x - 6
Use the method of completing the square
add/ subtract ( half the coefficient of the x- term )² to x² - x
y = x² + 2(- [tex]\frac{1}{2}[/tex]) x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] - 6
= (x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{25}{4}[/tex]
