Real World Quadratic Problems

You are snowboarding on a mountain at Breckenridge 23 ft up in the air. You are about to go off a jump. At 0 seconds, your standing up on the mountain up at 23 ft, then you begin to go off your jump. After one second, you are 37 ft above the ground. After 2 seconds, you are at 47 feet. After three seconds, you are at 53 feet. After four seconds, you reach your maximum height of 55 feet.

Select the equation that matches this situation.

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

The graph below shows the height, in feet, over time, in seconds, of a student's rocket. Use the graph to answer the questions below. What was the maximum height the rocket reached?

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$$h\left(x\right)=-4x^2+24x+10$$  
Part A: What is the starting height of the t-shirt?

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$$h\left(x\right)=-4x^2+24x+10$$
Part B: After how many seconds does the t-shirt reach its greatest height? Solve algebraically.

The height of the shirt based on the number of seconds, , is given by the equation
$$h\left(x\right)=-4x^2+24x+10$$
Part C: What is the t-shirt’s greatest height? Solve Algebraically

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation: 
$$f\left(t\right)=-3.5t^2+14t+3$$
Part B: What is the maximum height the ball reached after Prince threw it?

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation:
$$f\left(t\right)=-3.5t^2+14t+3$$
Part C: How long will it take for the ball to hit the ground?

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation:
$$f\left(t\right)=-3.5t^2+14t+3$$  
Part D: Prince is trying to throw the ball over a 19 foot high fence. Will his throw make it over?