Question 1042738
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 <font color=red>maximum</font>. 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 <font color=red>maximum</font> value is y = <font color=red>3</font> 


So the answer must be  <font color=red>choice B</font>