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.
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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
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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.
