Quadratic Transformations and Word Problems

2

A foul ball leaves the end of a baseball bat and travels according to the formula h(t) = 64t - 16t² where h is the height of the ball in feet and t is the time in seconds. How long will it take for the ball to reach a height of 64 feet in the air?

The graph of f was translated 4 units up to create the graph of g.

A student graphed f(x) = x on a graph and g(x) = f(x)+4 on the same coordinate grid. What statement describes how f and g are related?

The graph of f was stretched vertically stretched by a factor of 4 to create graph g.

A student graphed f(x) = x² on a graph and g(x) = 4f(x) on the same coordinate grid. What statement describes how f and g are related?

The graph of f was translated 4 units right to create function g.

A student graphed f(x) = x² then graphed g(x) = (x - 4)² on the same coordinate grid. What transformation was used to create function g?

256

Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin is above the water is modeled by the equation y = -16x²+ 96x + 112. Where x represents time in seconds. What is the maximum height of the coin? Hint: Graph the equation and find the maximum

10

At a swim meet, Janet dives from a diving board. Her position above the water is represented by the equation h(t) = -t² + 8t + 20, where t represents time in seconds and h(t) represents height in feet. How many seconds until Janet hits the water? (Hint: Height above water would equal zero)

9

How long is the object in the air?

1 and 1.25

What are the roots of the equation -2x²+5x=2x²-4x+5?

0 and 3/2

What are the roots of the function: 18-12t= -16t² + 12t + 18

2 and 2.5

What are the solutions to function g(x) = 2x²-9x+10

-3

What is the negative solution to the function f(x) = -x² - x + 6.

8

What is the positive solution to the function 0=¼x²-16