Answer:
y- value of the vertex for the given function \(\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)\) is 49.
Step-by-step explanation:
Given : The function \(\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)\)
We have to find the y- value of the vertex for the given function.
Consider the given function \(\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)\)
The vertex of the up-down facing parabola of the form \(y=a\left(x-m\right)\left(x-n\right)\) is the average of the zeros, \(x_v=\frac{m+n}{2}\)
Thus, here, m = 3 , n = -11 and a = 1
\(x_v=\frac{3+\left(-11\right)}{2}=-4\)
Thus, x- value of vertex is -4.
Now, put x = -4 to get y values
\(y_v=-\left(-4-3\right)\left(-4+11\right)=49\)
Thus, y- value of the vertex for the given function \(\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)\) is 49.
