Question

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

Answer 1

Answer:

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.