1

Quadratic Functions Project:

Parabolas Everywhere

Completed by: example by Mrs. B

Block: ____________

Mrs. Brkic’s class

Due date: _____________

Objectives of this project are…. I am interested to learn…

4 points

2

Pictures of Parabolas

pictures description Picture #1

This was taken during our trip to … This parabola is open up, so a must be positive. If placed on coordinate plane with same scale on x and y axes, I believe the leading coefficient will be between 0 and 1 as I believe there is a vertical shrink, the parabola looks quite wide

Picture #2

This was taken last Sunday … This parabola is open down so a must be negative. If placed on coordinate plane with same scale on x and y axes, I believe the leading coefficient will be between -1 and 0 as I believe there is a vertical shrink. My guess is, that this picture will be closest to parabola when I do the quadratic regression.

Picture #3

This was taken in my room the night before the pictures were due … This parabola is open up, so a must be positive. If placed on coordinate plane with same scale on x and y axes, I believe the leading coefficient will be between 0 and 1 as I believe there is a vertical shrink.

10 points Note – please remember to save all your pictures in FULL resolution, you will need them for DESMOS. Your pictures will have to have DECORATED SPRTAN HEAD with YOUR INNITIALS in it. Please place the Spartan head somewhere on the side so it doesn’t get in the way when using DESMOS

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Quadratic Regression #1

c. -Write the R2 (coefficient of determination, round to nearest hundredth or thousandth)

Identify the R2 value, then based on this choose which picture you are going to further analyze.

y = -.486x2 + .141x + 3.858 R2 = .992 After you have found the regression and rounded as requested, you will enter the equation of the regression in DESMOS as well. We will need to see the graph to decide if our picture is a parabola. How close are the shapes? How close is the R2 to 1?

5 points

Regression Calculations and Graphs

a. - A coordinate graph was accurately imported into Desmos over a copy of each parabola with 5 points

identified and regression equation modeled.

b. -Write the regression equation in standard form in DESMOS (round coefficients to nearest tenth or

hundredths)

4

Quadratic Regression #2

y = -.486x2 + .141x + 3.858 R2 = .992

5 points

5

Quadratic Regression #3

y = -.486x2 + .141x + 3.858 R2 = .997 This is my best parabola, R2 is closest to 1 and the graph traces the shape closely. I will be using this picture for the rest of the project:

5 points

Standard Form Using Quadratic Regression

Finding additional point

I am choosing x = -1 (must be an integerother

than the x coordinates we have used for the

regression)

Plug in x = -1 into regression equation (show

all work). Round the y coordinate to nearest tenth.

Plot the ordered pair into DESMOS

4 points

Standard Form using Quadratic Regression.

a. Choose an integer x-value that is not one of the five

previously picked points.

b. Plug it into the regression equation to get the y-

coordinate. Plot this point into Desmos. This should

lay directly on or close to your parabola.

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Vertex Form

Domain:

Range:

Increasing

interval:

Decreasing

interval:

(list all for

the parabola

you graphed)

Your DESMOS must include the two ordered points you used, both equations (vertex & standard), and the x

intercept ordered pairs you found with your calculations)

Finding equation of a parabola in Vertex form

(must include finding a and ALL work)

Work is shown in warm up key from “working on the project”

class. Look it up if you need

Rewriting equation from vertex to standard form

(must include finding ALL work)

Finding x intercept by solving equation when y=0

(You may start from vertex form and use suqre roots or standard form and use quadratic formula;

must include ALL work

24 points

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Intercept Form

Your DESMOS must include the two ordered points you used (nonzero x intercepts and additional integer

ordered pair), both equations (intercept & standard), and the ordered pairs you found for vertex with your

calculations)

Finding equation of a parabola in Intercept form

(must include finding a and ALL work)

Work is shown in warm up key from “working on the project”

class. Look it up if you need

Rewriting equation from vertex to standard form

(must include finding ALL work)

Finding vertex (You may start from intercept

form and use 2

p q or standard

form and use 2

b

a

quadratic

formula; must include ALL work)

20 points

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Conclusion and Reflection

Conclusion – Which of your picture were actual parabolas? Explain what an R2 value is and how you used it

to determine if your pictures could be accurately modeled by a parabola. Explain why certain U-shaped

models cannot be considered a parabola. Which of the methods was best at calculating the missing point(s)

and explain why?

Reflection -What do you feel that you learned from this project? What did you like most? What did you like

the least? What suggestions do you have for us to make this project better? What do you think you could have

done differently while working on this project?

10 points