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+((11)/(2))^2-((11)/(2))^2-26 \\ =(r+(11)/(2))^2-(121)/(4)-26=(r+(11)/(2))^2-(225)/(4). \end{gathered}`

Therefore the vertex of the given parabola is:

`(-(11)/(2),-(225)/(4)).`

Answer:

1)

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

2) Vertex:

`(-(11)/(2),-(225)/(4)).`