H(r) = (r + 1)(r +8)
1) What are the zeros of the function?
Write the smaller r first, and the larger r second.
smaller r =
larger r =
2) What is the vertex of the parabola?

1) The solutions are:

smaller r =  -8

larger r = -1

2) The vertex is .

Step-by-step explanation:

1) A zero of a function is an x-value that makes the function value 0.

To find the zeros of the function, first, we see that the linear factors of are

and .

If we set and solve for x, we get

Using the Zero factor principle, If ab = 0, then either a = 0 or b = 0, or both a and b are 0.

The solutions are:

smaller r =  -8

larger r = -1

2) The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a parabola.

To find the vertex of the function , first we need to find the standard equation of a parabola, which is,

Next, we find the r-coordinate of the vertex with the formula .

We know from the standard equation of a parabola that

So,

And the h-coordinate is

The vertex is .