SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x^2- 2x + 2 a. Minimum-1 b.

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Question 1046334: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x^2- 2x + 2
a. Minimum-1
b. Maximum 3
c. Minimum 3
d. Maximum-1

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

The function has a since the first term has a negative coefficient.
To find the maximum, you need to find the axis of symmetry first
To find the axis of symmetry, use this formula:


From the equation we can see that and ; so,



So the x-coordinate of the is , so lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate if is :




so, the is at (,)
So that means the functions highest value is which means the functions maximum is .
and your answer is: b. Maximum
check the graph:




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