SOLUTION: determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value
f(x) = 2xsquared + 2x - 6
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Question 222527: determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value
f(x) = 2xsquared + 2x - 6
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
.
From the coefficient associated with the x^2 term, in this case, it's a POSITIVE TWO. Since it is "positive" think "smiley face"-- so, it's a parabola that's opens upwards. If it was "negative" think "sad face" -- so, it's a parabola that's opens downwards.
.
Since the coefficient is +2, it opens upwards thus the function will have a MINIMUM.
.
One way to find the vertex, is by completing the square. Doing so you will get it into the "vertex form" of the equation:
y= a(x-h)2+k
where
(h,,k) is the vertex
.
.
Therefore, the vertex is at (-1/2, -13/2)
or
(-.5, -6.5)
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