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

Algebra ->  Functions -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+2x%5E2+%2B+2x+-+6+
.
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
.
f%28x%29+=+2x%5E2+%2B+2x+-+6+
f%28x%29+=+2%28x%5E2+%2B+x+%2B+__%29++-+6+
f%28x%29+=+2%28x%5E2+%2B+x+%2B+1%2F4+%29++-+6+-+1%2F2
f%28x%29+=+2%28x+%2B+1%2F2%29%5E2++-+13%2F2+
f%28x%29+=+2%28x+-+%28-1%2F2%29%29%5E2++%2B+%28-13%2F2%29
.
Therefore, the vertex is at (-1/2, -13/2)
or
(-.5, -6.5)