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.

Algebra ->  Functions -> 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.       Log On


   

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(20855) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-x%5E2-+2x+%2B+2
The function has a maximum since the first term -x%5E2 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:
x=-b%2F%282a%29

From the equation y=-x%5E2-2x%2B2 we can see that a=-1 and b=-2; so,
x=-%28-2%29%2F%282%28-1%29%29
x=2%2F%28-2%29
highlight%28x=-1%29
So the x-coordinate of the vertex is x=-1, so lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate y=-x%5E2-2x%2B2 if is x=-1:
y=-%28-1%29%5E2-2%2A%28-1%29%2B2
y=-1%2B2%2B2
y=-1%2B4
highlight%28y=3%29
so, the vertex is at (-1,3)
So that means the functions highest value is 3 which means the functions maximum is 3.
and your answer is: b. Maximum 3
check the graph: