SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x2 - 3x - 8

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x2 - 3x - 8      Log On


   

Question 362971: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 3x - 8
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The coefficient of x%5E2 is negative, so the graph is a parabola facing downward, and hence the function has a maximum. The maximum value happens at x+=+-b%2F%282a%29+=+--3%2F%282%2A-1%29+=+3%2F-2+=+-3%2F2. The maximum value is -%28-3%2F2%29%5E2+-+3%2A%28-3%2F2%29-8+=+-9%2F4%2B9%2F2-8+=+9%2F4-8+=+-23%2F4.