A baseball player steps up to bat. He swings and hits the ball along the foul line. The height in feet, y, of the ball x seconds after the player hits it is given by the equation y = -16x + 95x + 6

Question

How long until the ball hits the ground and the umpires call the ball fair or foul?

Answer 1

y = -16x² + 95x + 6, where x is time (in seconds) and y is the height (in feet).

We want to know how long will it take for the baseball to hit the ground after the umpire calls it fair or foul. This refers to finding the x-intercepts (solutions). When the baseball reaches the ground, the height is at zero.

Factor the quadratic equation using the greatest common factor (GCF = -1). Then use the diamond or box method to solve for x. Apply the zero product property.

-16x² + 95x + 6 = 0

-(16x² - 95x - 6) = 0

-(16x² - 96x + x - 6) = 0

-[16x(x - 6) + 1(x - 6)] = 0

-(16x + 1)(x - 6) = 0

x = -1/16 or x = 6. Since we can't have a negative number in time, the only solution that will work is x = 6. That means at 6 seconds, the baseball will land on the ground.