Answer:
y = (x - [tex]\frac{3}{2}[/tex] )² - [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
y = x² - 3x + 1
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 3x
y = x² + 2(- [tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] + 1
= (x - [tex]\frac{3}{2}[/tex] )² - [tex]\frac{9}{4}[/tex] + [tex]\frac{4}{4}[/tex]
= (x - [tex]\frac{3}{2}[/tex] )² - [tex]\frac{5}{4}[/tex] ← in vertex form
