Answer :
Answer:
y = (x + [tex]\frac{3}{2}[/tex] )² - [tex]\frac{5}{4}[/tex]
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 = x² + 3x + 1
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{5}{4}[/tex]