Building Quadratic Functions to Describe Situations

The height of a baseball, in feet, is modeled by the function $$h$$ given by the equation $$h(t) = 3 + 60t - 16t^2$$ . The graph of the function is shown. About when does the baseball reach its maximum height? About how high is the maximum height of the baseball? About when does the ball hit the ground?

The height of a diver above the water is given by $$h(t) = - 5t^2 + 10t + 3$$ , where $$t$$ is time measured in seconds and $$h(t)$$ is measured in meters. Select all statements that are true about the situation.

Technology required. Two rocks are launched straight up in the air. The height of Rock A is given by the function $$f$$ , where $$f(t) = 4 + 30t - 16t^2$$ . The height of Rock B is given by $$g$$ , where $$g(t) = 5 +20t - 16t^2$$ . In both functions, $$t$$ is time measured in seconds and height is measured in feet. Use graphing technology to graph both equations. Determine which rock hits the ground first and explain how you know.

Han accidentally drops his water bottle from the balcony of his apartment building. The equation $$d=32-5t^2$$ gives the distance from the ground, $$d$$ , in meters after $$t$$ seconds. Complete the table and plot the data on the coordinate plane. Is the water bottle falling at a constant speed? Explain how you know.

Here is a pattern of dots. Complete the table. How many dots will there be in Step 10? How many dots will there be in Step $$n$$ ?

A rocket is launched in the air and its height, in feet, is modeled by the function $$h$$ . Here is a graph representing $$h$$ . Select all true statements about the situation.

A baseball travels $$d$$ meters $$t$$ seconds after being dropped from the top of a building. The distance traveled by the baseball can be modeled by the equation $$d = 5t^2$$ . Is the baseball traveling at a constant speed? Explain how you know.

A small ball is dropped from a tall building. Which equation could represent the ball’s height, $$h$$ , in feet, relative to the ground, as a function of time, $$t$$ , in seconds?

The function $$f$$ represents the revenue in dollars the school can expect to receive if it sells $$220-12x$$ coffee mugs for $$x$$ dollars each. Here is the graph of $$f$$ . Select all the statements that describe this situation.

Technology required. A small marshmallow is launched straight up in the air with a slingshot. The function $$h$$ , describes the height of the marshmallow in meters as a function of time, , in seconds since it was launched. Use graphing technology to graph the function $$h$$ . About when does the marshmallow reach its maximum height? About how long does it take before the marshmallow hits the ground? What domain makes sense for the function $$h$$ in this situation?