Answer:
(2,-16)
Step-by-step explanation:
One way to find the vertex is as follows:
First, we see that the x-intercepts are 6 and -2.
(to see this, we use the fact that the x-intercepts are found by letting y i.e. f(x) = 0. Then we solve each of the factors equal to 0. so i.e.
x-6 = 0
x = 6.
Similarly, x+2 = 0, so x= -2).
Now that we know the x-intercepts, we can use the symmetry property of a quadratic to see the x-coordinate of the vertex occurs mid-way between -2 and 6. So i.e at (6+-2)/2 = 2.
Lastly, we put x = 2 into the equation to find the y-coordinate:
f(2) = (2-6)(2+2) = -4 x 4 = -16.
So the vertex is (2,-16)
