Question #967d4

1 Answer
Apr 27, 2017

see explanation below

Explanation:

Y = -x^2 + 4 x -12

we can find it vertex by using completing a square.
Y = -(x^2 - 4x) - 12
Y = -(x -2)^2 +(-2)^2 -12
Y = -(x -2)^2 + 4 -12
Y = -(x - 2)^2 - 8
Therefore it vertex is maximum at (2, -8)

To find x-intercept, plug in Y = 0, but since it maximum is -8 this equation has no x-intercept. We can check using b^2-4ac < 0 where, a =-1, b = 4 and c = -12
(4)^2 -4(-1)(-12) = 16 -48 < 0

To find y-intercept, plug in x = 0,
Y = -(0 - 2)^2 - 8
Y = -4 - 8 = -12 ->y-intercept