Question

Determine whetherf(x) = 6x2+ 12x + 8 has a minimum or maximum value and find thevalue of the minimum or maximum. Also, find the axis of symmetry

Answer 1

Answer:

• minimum value: 2
• axis of symmetry: x = -1

Step-by-step explanation:

A graphing calculator can answer this very quickly. The graph shows the minimum is 2, at x=-1. The axis of symmetry is the vertical line through that point so is x = -1.

__

The extreme value of the quadratic ax^2 +bx +c is found at x = -b/(2a). Your quadratic has a=6 and b=12, so the extreme value is located on the line of symmetry at ...

  x = -12/(2·6)

  x = -1 . . . . . . . . . . line of symmetry; x-coordinate of vertex

__

The leading coefficient of this even-degree polynomial is positive, so we know it opens upward. That means the vertex is a minimum.

The value of the function at the vertex is ...

  f(-1) = 6(-1)^2 +12(-1) +8 = 6 -12 +8 = 2

The minimum value is 2.