Question #967d4

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1 Answer
salamat
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

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