SOLUTION: Please help me solve this equation: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = 2x^2

Algebra ->  College  -> Linear Algebra -> SOLUTION: Please help me solve this equation: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = 2x^2      Log On


   

Question 1049030: Please help me solve this equation:
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = 2x^2 - 2x
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Coefficient on the leading term is POSITIVE 2. This parabola is concave upward, or convex downward; the vertex is a minimum.

2x%5E2-2x=0
2x%28x-1%29=0
x%28x-1%29=0
The x-intercepts are at 0 and 1. Because of symmetry the vertex (minimum point) will be at the exact middle of 0 and 1; or at x=1%2F2.

f%281%2F2%29=2%281%2F2%29%5E2-2%281%2F2%29-----compute this.