Log inSign up for FREE
Library

04 Applications of Quadratic Equations 1

Last updated over 4 years ago
18 questions
Today you will be completing application questions for quadratic equations.
YOU WILL NEED YOUR GRAPHING CALCULATOR.

Look below at all the important points on a graph, and what information they provide.
To be able to graph most application questions, you need to learn how to change the table set and the window of your graph. Most things hit the ground within seconds... So you don't need to look at any negative numbers and you won't need to have the x-axis go up to 10.

Table Set: This adjust the x input numbers. Things go up and fall down fast. You will often need tenths of a second to look at.
Hit the following keys on your calculator.
2nd Function
"Window button" It says table set above it
TblStart = 0
Tbl = 0.1
This will give you the height for every tenth of a second.

Window (What you see when it is graphed) Many things go up much higher than 10. This will allow you to see what the parabola looks like.
Hit the following keys on your calculator.
Window button
Xmin = 0 Nothing happens before 0 time.
Xmax = 5? 3? 10? Since this represents time, it won't be too high.
Xscl = 0.1 (This will allow every tenth of a second to show) - If you don't need tenths, keep it at one.
Ymin = 0
Ymax = ??? (This is hard to say. If it is a cannon or a tall building, then you need to figure out how high this parabola is going to go. If it is a flea jumping... well you don't need the y-axis to go very high.)
Yscl = ??? (If you are graphing up to 200, you only need to see a little hash mark every 50. You again need to decide based on the question.)

You will need to see what equation you are using and need to adjust. You may cut off the top of the parabola, then you need to make the Ymax higher. You may need to see only up to 3 seconds, you change the Xmax.

Below are two videos to help with this if you need more assisstance.
1

An object is dropped from a height of 100 feet, the function
gives the height of the object after t seconds.

Graph this function below. You will need to adjust your table set to every tenth of a second to help you be accurate. You will also need to adjust your height on the viewing window.

1

What is the height of the object at 1 second?

1

At what time exactly does the object hit the ground?

1

At what time is the object 64 ft in the air?

1

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
Graph the function below. You will need to adjust your height on the viewing window.

1

How long will it take for the rocket to return to the ground?

1

After how many seconds will the rocket be 112 feet above the ground? There are TWO answers, the rocket goes up and then comes down. Use the word "and" in between the two times.

1

How long will it take the rocket to hit its maximum height?

1

What is the maximum height for the rocket?

1

The storage building shown can be modeled by the graph of the function
where x and y are measured in feet.

Fill in the missing numbers from each coordinate on the diagram below.

1

What is the height h of the highest point of the building?

1

How wide is the storage bin at its base?

1

A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function below, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet.
Graph this function on the following page.

1

What is the vertex of this function?

1

Interpret the meaning of this vertex in the context of the problem.

1

The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Explain your answer based on the graph.

1

A flea's jump can be calculated by the function below.
How high can a flea jump at 0.25 seconds?

1

A frog's leap is able to be calculated by the function below.
At what time is the frog at his highest?