Question

Which statement is true about the extreme value of the given quadratic equation? y = -3x2 + 12x − 33

Answer 1

Answer:

The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

Given

$y =-3x^2 + 12x - 33$

Required

The true statement about the extreme value

First, write out the leading coefficient

$Leading = -3$

$-3 < 0$ means that the function would be a downward parabola;

Downward parabola always have their vertex on top of the parabola and as such, the function has a maximum value.

The maximum value is:

$x = -\frac{b}{2a}$

Where:

$a= -3; b =12; c =-33$

So, we have:

$x = -\frac{12}{2 * -3}$

$x = -\frac{12}{-6}$

$x =2$

Substitute $x =2$ in $y =-3x^2 + 12x - 33$

$y = -3*2^2 + 12 * 2 - 33$

$y = -21$

Hence, the maximum is -21.