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


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.