Quadratic Opener: The parts of a Parabola

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

This question is asking about which vocabulary word?

• Minimum

• x intercept

• maximum

• zero

The previous question asked about maximum height. Explain how you chose your answer.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

This question is asking about which vocabulary word?

• minimum

• y intercept

• x-intercept

• axis of symmetry

The previous question asks about when the diver would hit the water? What word did you chose to represent the water and why?

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

This question asks about which vocabulary word?

• minimum

• maximum

• axis of symmetry

• none of the above

Question 5 asks about when you would be 16 feet above the water. How did you make sense of this?

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

Which vocabulary word would contain the location of maximum profit?

• the vertex

• the axis of symmetry

• one of the zeroes

• the y-intercept

What does maximum profit mean to you and what word did you use to visualize maximum profit?

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

The question is asking about the...

• vertex

• zero

• axis of symmetry

• y-intercept

If you are asked about the ground or the water surface, what words could represent that and why?