Question

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

Answer 1

h = -
`(3)/(2)`

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(
`(3)/(2)` )x +
`(9)/(4)` -
`(9)/(4)` ) + 11

= 2(x +
`(3)/(2)` )² -
`(9)/(2)` + 11

= 2(x +
`(3)/(2)` )² +
`(13)/(2)` ← in vertex form

with h = -
`(3)/(2)`