SOLUTION: i need help with this problem f(x)=-2x^2-16x-33......does it have a minimum or maximum value? where does the minimum or maximum value occur? and what is the maximum or minimum valu

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Question 639284: i need help with this problem f(x)=-2x^2-16x-33......does it have a minimum or maximum value? where does the minimum or maximum value occur? and what is the maximum or minimum value? Any help would be greatly appreciated...thanks and God Bless
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
a = -2, b = -16, c = -33
-b%2F2a+=+-%28-16%29%2F%282%28-2%29%29+=+-4

Vertex is (-4,-1).
The graph opens downward because a<0, therefore it has a maximum value when x = -4. The maximum value is -1.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B-16x%2B-33+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-16%29%5E2-4%2A-2%2A-33=-8.

The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-16%2Ax%2B-33+%29