Question

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

Answer 1

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

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 = -(b)/(2a)`

Where:

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

So, we have:

`x = -(12)/(2 * -3)`

`x = -(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.