Question

You might need: Calculator h(r) = 72 +11r - 26 1) What are the zeros of the function? Write the smaller r first, and the larger r second.

Answer 1

1) Notice that:

$r^2+11r-26=r^2+13r-2r-2(13).$

Grouping like terms we get:

$\begin{gathered} r^2+13r-2r-2(13)=r(r+13)-2(r+13) \\ =(r-2)(r+13). \end{gathered}$

Therefore:

$h(r)=(r-2)(r+13).$

Then the zeros of h(r) are:

$r=2\text{ and }r=-13.$

2) Notice that:

$\begin{gathered} h(r)=r^2+11r-26=r^2+11r+(\frac{11}{2})^2-(\frac{11}{2})^2-26 \\ =(r+\frac{11}{2})^2-\frac{121}{4}-26=(r+\frac{11}{2})^2-\frac{225}{4}. \end{gathered}$

Therefore the vertex of the given parabola is:

$(-\frac{11}{2},-\frac{225}{4}).$

Answer:

1)

$\begin{gathered} smaller\text{ r=-13,} \\ larger\text{ r=2.} \end{gathered}$

2) Vertex:

$(-\frac{11}{2},-\frac{225}{4}).$