Question 1042738: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 2x + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! f(x) = -x^2 - 2x + 2
-x^2 - 2x + 2 has the leading coefficient of -1. The negative leading coefficient means that the parabola opens downward.
The parabola opening downward is like an upside down bowl shape. So this function has a maximum. Think of it as the peak of the mountain.
In the case of -x^2 - 2x + 2, the values of a,b,c are
a = -1
b = -2
c = 2
Plug a = -1 and b = -2 into x = -b/(2a) to get
x = -b/(2a)
x = -(-2)/(2(-1))
x = -(-2)/(-2)
x = 2/(-2)
x = -1
So the max y value occurs when x = -1. Plug x = -1 into the original function to find the corresponding value of y.
f(x) = -x^2 - 2x + 2
f(-1) = -(-1)^2 - 2(-1) + 2
f(-1) = -(1) - 2(-1) + 2
f(-1) = -1 - 2(-1) + 2
f(-1) = -1 +2 + 2
f(-1) = 1 + 2
f(-1) = 3
When x = -1, the corresponding y value is y = 3
The two values pair up to get this point (-1,3)
The vertex is at the point (-1,3)
Therefore, the maximum value is y = 3
So the answer must be choice B
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