Maths-

General

Easy

Question

# A water balloon is tossed into the air. The function h(x) = -0.5(x-4)^{2} + 9 gives the height, in feet, of the balloon from the surface of a pool as a function of the balloon’s horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

Hint:

### The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.

## The correct answer is: (4, 9)

### We have given a function of water balloon tossed into air,

h(x) = -0.5(x-4)^{2} + 9

The given equation is in the vertex form

We know vertex is the point at maximum height .

And y coordinate of vertex is the maximum height of the ball

On comparing with the vertex form we get that

h = 4

k = 9

Therefore, here vertex is (4, 9)

Here, we have y-coordinate as 9

So, the maximum height of ball is 9

We have given the ceiling height as 12 ft

So the height of ceiling is more than maximum height of ball , so ball will not hit the ceiling.

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