Real world quadratic problems: superimposed on the coordinate plane.

#1. A diver jumps off of a platform 14 feet above water. Her dive is modeled by the quadratic equation x2 – 9x +14 where y is her height above water in feet and x is the time in seconds from her jump.

Convert the diver’s quadratic equation from

standard to x-intercept form. Sketch the graph.

Using unit vocabulary, describe the point where

the diver is standing on the platform with

reference to the coordinate plane.

How many seconds is the diver in the air before she enters the pool?

At what time(s) does she break the surface of the water?

(relate back to quadratic vocabulary covered in the unit)

What is her height above the water at this/these point(s)?

How many seconds in total is the diver under water?

What is the meaning of the vertex in this real world problem?

Is she further beneath the water 4 seconds after diving or 5 seconds after diving? Use the equation to justify your answer?

# 2. A football kicker is trying to make the extra point from 14 yards away (42 feet). To make the goal, the football must clear the 10-ft goal post stand. His kick is modeled by the quadratic equation y = -.04x(x – 50).

Name the form of the equation modeling the kick.

Does the concavity (opening up or down) of the parabola make sense in the context of this real world problem? Explain in the complete sentence.

Will the kick make the extra point from the distance of 42 feet away?

Does the distance of the kicker affect his chances of making the goal? Explain in reference to the quadratic equation provided.

How far away from the kicker would the ball hit the ground, what does this mean in terms of the graph?

Challenge: give an exact distance (with respect to your equation) from which the kicker could clear the goal.

Challenge: What was the maximum height of the kick?

#3. A model rocket is launched in the air according to the trajectory shown on the graph where y is the height in yards and x is the time in seconds since it’s launch.

Write the equation of the rocket launch using vertex form.

What do the zeroes represent in the context of the real world problem?

How many seconds in the air before the rocket changes direction? Using unit vocabulary, describe the point where the rocket changes direction in the air.

What is the maximum height of the rocket?

How many seconds after take off does the rocket reach its maximum height?

Looking at the graph, identify an (x, y) point where x and y are both negative. Explain why this point on the parabola does not make sense in the context of the rocket launch.

# 4. You are the owner of a company whose profit is determined by the equation y = –x2 +20x (y = -(x- 10)2+100 where x is the number of workers and y is the amount of company profit in thousands of dollars.

X – the number of workers / Y = –x2 +20x / Y-profit in thousands of dollars
0
6
8
10
12
20
25

If you hire zero workers, how much profit do you make?

In reference to your table, did increasing the number of workers at every interval result in increased profits?

According to your table, what is the maximum number of workers you would want to employ as the company owner? explain.

Suppose you were currently operating 8 workers and decided to hire 3 extra workers. How would the additional workers affect the profitability of your company. Is it worth it to hire them? Explain.

From the table, what are the solutions of this

real world quadratic? What do the solutions

represent in the context of a real world

business model?

Could the profitability equation be written as

Y = -1(x – 0) (x – 20) ?

Use the coordinate plane to sketch the graph of your company’s profitability curve.