Kalob throws a ball from a window. The relationship between X, the balls distance in feet from the building, and y, the height of the ball in C, can be found using this equation.

Question

Y =-16x^2 +48x + 64

The ball will land on the ground when it is? Feet away from the building. The maximum height of the ball will reach is? Feet.

Answer 1

When the ball hits the ground the height y will be zero so solve -16x^2 + 48x +64 = 0

you can factor out a -16 which gives you -16( x^2 -3x -4)=0

x^2 -3x-4 =0

(x-4)(x+1) =0

x=4 or -1 but you can discard -1 in the context of this problem (would require you to go back in time)

So the ball will be 4 feet from the building

The maximum height is at the vertex of this downward facing parabola

The X coordinate of the vertex is at -b/2a or -48/-32 = 3/2

when x=3/2 y= -16(3/2)^2 +48(3/2) +64= -16(9/4) + 72 +64= -36+72+64= 100

so maximum height is 100 ft