Answer:
h = - [tex]\frac{3}{2}[/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
Given
y = 2x² + 6x + 11 ( factor out 2 from the first 2 terms )
= 2(x² + 3x) + 11
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 3x
y = 2(x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] ) + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² - [tex]\frac{9}{2}[/tex] + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{13}{2}[/tex] ← in vertex form
with h = - [tex]\frac{3}{2}[/tex]
