A water balloon is tossed into the air. The function h(x)=-0.5(x-4)squared +9 gives the height, in the feet, of the balloon from the surface of a pool as a function of the balloons horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

No, the maximum height that the balloon can reach is 9ft.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

The function h(x) =-0.5(x-4)² +9, is a Quadratic Function in the Vertex form.

Vertex form: f (x) = a(x - h) 2 + k

Where:

(h, k) is the vertex of the parabola-h is the horizontal shift (how far left, or right, the graph has shifted from x = 0).  k represents the vertical shift (how far up, or down, the graph has shifted from y = 0).  

In this case a = -0.5, it means that the parabola opens downward and has a maximum point at the vertex.

So, the maximum height that the balloon can reach is k=9ft.

9 ∠ 12

The balloon will not hit the ceiling 12 ft above the pool.

Feel free to ask for more if needed or if you did not understand something.

The answer石A)十七.hope thisへlps！