Quadratics Functions in Context

A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression

-16t² + 40t + 3.

What is the meaning of the 3 in the expression?

• The ball took 3 seconds to reach its maximum height.

• The ball took 3 seconds to reach the ground.

• The ball was thrown from a height of 3 feet.

• The ball reached a maximum height of 3 feet.

The function g(x) = -16x² + vx + h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet. 

A model rocket is launched off the ground at an initial velocity of 80 feet per second. Create a function that can be used to describe the flight of the model rocket.

Mathematical Equivalence

ON

The function g(t) = -16x² + vx + h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet. 

A model rocket is launched off the ground at an initial velocity of 80 feet per second.

What domain makes sense for the function in this context?

• 0 ≤ t ≤ 5

• 0 ≤ t ≤ 100

• all real numbers

• all positive numbers

Sort the following cards based on the characteristic of a quadratic function that each scenario is referencing.

• This scenario is looking for the y-value of the vertex.

• Ashley threw a ball into the air. She wonders how high the ball went.

• This scenario is looking for the positive zero/x-intercept.

• Jalencia is trying to find how many seconds it will take a golf ball to get to its highest point after being hit on the golf course.

• This scenario is looking for the x-value of the vertex.

• Lindsey wants to know how long her toy rocket will be in the air after she lights the fuse to launch it from a 1.5-foot launch pad.