Question

Need help answering all these questions for the red bird.Quadratic equation of the red bird: h(x) = -x^2 + 10x - 9King Pig located at the point (11,9) Moustache Pig located at the point (10,4)

Answer 1

`h(x)=-x^2+10x+9`

The maximum heigh is located at the vertex. The vertex is:

`\begin{gathered} V=(h,k) \\ where: \\ h=-(b)/(2a)=-(10)/(2(-1))=5 \\ k=h(h)=-(5^2)+10(5)+9=-25+50-9=16 \end{gathered}`

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:

`\begin{gathered} -x^2+10x-9=x^2-10x+9=(x-9)(x-1) \\ so \\ x=1 \\ or \\ x=9 \end{gathered}`

So, the distance traveld is:

`\Delta x=x2-x1=9-1=8`

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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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