SOLUTION: Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value. Please show all of your work. f(x) = -2x²+2x

Algebra ->  Functions -> SOLUTION: Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value. Please show all of your work. f(x) = -2x²+2x      Log On


   

Question 465221: Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value. Please show all of your work.
f(x) = -2x²+2x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-2x%5E2%2B2x
Remember that when the x%5E2 in the parabola equation is negative, the parabola opens downwards. Therefore, it has a maximum value.
ANSWER: The quadratic function has a MAXIMUM value.
Remember that the vertex of a parabola occurs at (h, k).
Given: f%28x%29+=+-2x%5E2%2B2x
Means: a+=+-2, b+=+2, c=0
h+=+-b+%2F+2a
h+=+-2+%2F+2%28-2%29
h+=+-2+%2F+-4
h+=+1+%2F2

k+=+%28-b-4ac%29+%2F+4a
k+=+%28-2-4%28-2%29%2A0%29+%2F+4%28-2%29
k+=+-2+%2F-8
k+=+1%2F4

the vertex: is at (1+%2F2, 1+%2F4)
+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+5%2C+-2x%5E2%2B2x%29+