[tex]h(x)=-x^2+10x+9[/tex]
The maximum heigh is located at the vertex. The vertex is:
[tex]\begin{gathered} V=(h,k) \\ where: \\ h=-\frac{b}{2a}=-\frac{10}{2(-1)}=5 \\ k=h(h)=-(5^2)+10(5)+9=-25+50-9=16 \end{gathered}[/tex]
Therefore, the maximum height is the y-coordinate of the vertex which is 16.
The axis of symetry is located at the x-coordinate of the vertex,so:
The axis of symetry is x = 5.
The distance traveled can be found using the roots:
The roots of the equation are:
[tex]\begin{gathered} -x^2+10x-9=x^2-10x+9=(x-9)(x-1) \\ so \\ x=1 \\ or \\ x=9 \end{gathered}[/tex]
So, the distance traveld is:
[tex]\Delta x=x2-x1=9-1=8[/tex]
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The bird will hit the ground on the second root, so:
The point where it hits the grund is (9,0).
The starting point is located at the first root, so the starting point is:
(1,0)
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