# Question #967d4

Apr 27, 2017

see explanation below

#### Explanation:

$Y = - {x}^{2} + 4 x - 12$

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

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

To find y-intercept, plug in $x = 0$,
$Y = - {\left(0 - 2\right)}^{2} - 8$
$Y = - 4 - 8 = - 12$ $\to$y-intercept