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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