Answer:
The equation has a maximum value with a y-coordinate of -21.
Step-by-step explanation:
Given
[tex]y =-3x^2 + 12x - 33[/tex]
Required
The true statement about the extreme value
First, write out the leading coefficient
[tex]Leading = -3[/tex]
[tex]-3 < 0[/tex] 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:
[tex]x = -\frac{b}{2a}[/tex]
Where:
[tex]a= -3; b =12; c =-33[/tex]
So, we have:
[tex]x = -\frac{12}{2 * -3}[/tex]
[tex]x = -\frac{12}{-6}[/tex]
[tex]x =2[/tex]
Substitute [tex]x =2[/tex] in [tex]y =-3x^2 + 12x - 33[/tex]
[tex]y = -3*2^2 + 12 * 2 - 33[/tex]
[tex]y = -21[/tex]
Hence, the maximum is -21.
Answer:
The equation has a maximum value with a y-coordinate of -21.
Step-by-step explanation:
