The parabola y= -x^2 + 8x + 2 will have:

a) a maximum of 16
b) a minimum of 16
c) a minimum of -46
d) a maximum of -18
e) a maximum of 18

explain :)

I'm assuming that you are not in Calculus, so I will do this algebraically.

y - 2 = -x^2 + 8x

y - 2 = -1(x^2 - 8x)

y - 2 + ? = -1 (x^2 - 8x + 16) (-8/2)^2 = 16

y - 2 - 16 = -1(x-4)^2 distributed -1*16 to get -16 on left side

y - 18 = -1(x-4)^2

The vertex is (4,18) and the parabola is opening downward since the x^2 term is negative, so 18 is a maximum and E is your answer.

E

Jen

x = -b/2a = 8/2 = 4
y(4) = -16 + 32 + 2 = 18
a = -1 < 0 , parabola opens down, hence a maximum at vertex(4 , 18)