Question

If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)

Answer 1

Answer:

h = - $\frac{3}{2}$

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($\frac{3}{2}$ )x + $\frac{9}{4}$ - $\frac{9}{4}$ ) + 11

  = 2(x + $\frac{3}{2}$ )² - $\frac{9}{2}$ + 11

  = 2(x + $\frac{3}{2}$ )² + $\frac{13}{2}$ ← in vertex form

with h = - $\frac{3}{2}$