Question

g(r)=−(r+11)(r+14)

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

(___,____)

Answer 1

Answer:

The zeros are

Larger $r=-11$

Smaller $r=-14$

2)The vertex is (-12.5,-2.25)

Step-by-step explanation:

The given function is:

$g(r)=(r+11)(r+14)$

This function is already in the factored form therefore it is easy to find the zeros,

$(r+11)(r+14)=0$

Either $(r+11)=0$ or $(r+14)=0$

The zeros are $r=-14$ or $r=-11$

b) The expanded form of the given function is:

$g(r)=r^2+25r+154$

We obtain the vertex form by completing the square:

$g(r)=r^2+25r+(\frac{25}{2})^2+154-(\frac{25}{2})^2$

The vertex form is:

$g(r)=(r+\frac{25}{2})^2-(\frac{9}{4}$

Therefore the vertex is (-12.5,-2.25)