Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16. How many seconds after being thrown will the ball hit the ground?
Q. Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16. How many seconds after being thrown will the ball hit the ground?
Understand the problem: Understand the problem.We need to find the time when the ball hits the ground. This happens when the height h(x) is equal to 0.
Set up the equation: Set up the equation to solve for x when h(x)=0.0=−(x−2)2+16
Solve for x: Solve the equation for x.First, move the terms around to isolate the squared term.(x−2)2=16
Take square root: Take the square root of both sides of the equation.x−2=±16
Find positive solution: Solve for x.x=2±4
Find positive solution: Solve for x.x=2±4Find the positive solution for x since time cannot be negative.x=2+4x=6
More problems from Interpret parts of quadratic expressions: word problems