Answer:
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 .