1) Notice that:
[tex]r^2+11r-26=r^2+13r-2r-2(13).[/tex]Grouping like terms we get:
[tex]\begin{gathered} r^2+13r-2r-2(13)=r(r+13)-2(r+13) \\ =(r-2)(r+13). \end{gathered}[/tex]Therefore:
[tex]h(r)=(r-2)(r+13).[/tex]Then the zeros of h(r) are:
[tex]r=2\text{ and }r=-13.[/tex]2) Notice that:
[tex]\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}[/tex]Therefore the vertex of the given parabola is:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]Answer:
1)
[tex]\begin{gathered} smaller\text{ r=-13,} \\ larger\text{ r=2.} \end{gathered}[/tex]2) Vertex:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]