Quadratic Project
1. The project is due on December 14th for all classes. Project turned in after December 18th will not
receive a passing grade.
2. You may only receive help from your partner and from your math teacher. You may not receive help
from anyone else. In addition to turning in the final project, you must submit scrap work indicating
that each partner did each part. Projects done with partners will have higher deductions for mistakes.
The project will count as a test grade. Neatness counts.
3. You may use a graphing calculator to help you see the work. However you must calculate all answers
and show all work. At least 50% deductions will be taken for work not shown.
Part 1: The Coin Fountain (study of parabolic curves through design of water arcs) <150 points>
You have been hired to design the water arc of a coin fountain. The pool of the fountain is 20 feet wide, and
the water arc it to be greater than 6 feet tall but less than 50 feet tall. It cannot start at zero or end at 20.
(You also can’t use 1 and 17). You will need to determine the locations of the launch and landing points and
maximum height of the arc. Also, you will need to write equations of the arc in relation to the horizontal
distance along the pool.
1. On graph paper, place the side view of your fountain in a first quadrant graph. Have the surface of the
pool correspond to the x-axis with the left side of the origin. On graph paper, show the coordinate of
the launching point, landing point, and maximum point and include all pertinent data points from the
questions below. Be sure to have a properly capitalized title and labels with units.
2. Using the equation y = a(x – root)(x – root), write the equation. (Hint: Plug in the highest point to find
‘a’) (<If ‘a’ is -1 then do the problem again>).
3. State the launch, maximum height, and landing points as coordinates. Also label them with
appropriate mathematical words (y-intercept etc…) on your work paper.
4. Convert equation #2 to y=ax2 + bx + c form. Label what ‘c’ represents and indicate how it matches to
your graph.
5a Factor equation #4 to find the landing and launch points algebraically.
5b Solve EQUATION FROM #4 > 0
6. Use the quadratic formula to find the launch and landing points from #4.
7. Solve #4 by completing the square to find the launch and landing points from #4.
8. Write equation #4 in vertex form and state the vertex based on the equation.
9a. Find the axis of symmetry and draw it on your graph.
9b. How high will the graph be 2 feet horizontally from your launch point? Show work.
(If your launch point is 5 feet then you want to know the height at 7 feet)
10. List the domain, range, practical domain, and practical range of the graph.
(Practical domain/range are numbers that are applicable to your problem. Ex: If John were to jump
from a 10 foot cliff and land in the water after 1 second then his practical domain is 0<t<1, practical
range is 0<y<10; domain is all reals and range is y<10.)
11. Find the focus and directrix. Plot them on the graph.
12. Find the equation of the inverse of the graph.
Example: y = -5(x + 3)2 – 10

x =-5(y + 3)2 – 10
 x+ 10 = -5(y+3)2  (x+10)/-5 = (y+3)2  y= ±√(𝑥+10)
-3
−5
13. Find the exact horizontal distance from the origin on when the graph will be 5 feet tall.
Verify graphically. (Also show the decimal estimation of the exact distance.)
14. Determine the exact value of ‘a’ that will produce a 50 foot arc for the chosen launch and landing
point. Compare/contrast/explain the new ‘a’ versus the former ‘a’. Give the equation (vertex form)
and graph the arc in a different color.
15. Create a second arc (in y= ) form. Give the equation of the second arc and your algebraic
calculations for the point(s) of intersection. Make sure that ‘a’ of your second graph is different from
the ‘a’ in the first graph. Graph the arc in a different color. (Hint: put both equations in standard
form, set them equal to each other and then solve.
Rubric: Each part is worth 9 points with the remaining 15 points coming from neatness. Label each part with
the work you turn in.
Part 2: Water Fountain (or Projectile) Project (50 points)
Directions:
1) Take a picture of the fountain from a distance; and a close-up with the fountain turned on; Bring a printed
picture of the turned-on fountain to class.
2) Create a graph grid for the picture. Let y-axis is the where the water is released from and the x-axis is the
water basin.
3) Using a ruler in cm, calculate the vertex, another point on the water graph, and where it hits the ground
both ahead of the faucet and where it would hit if the path went behind the spicket.
4) Using vertex form and the other point, calculate the equation in vertex form.
5) From vertex form, show how to get to standard form.
6) From standard form, show how to the estimated roots algebraically. Verify the roots graphically.
Final Product Each group must submit a 8.5” x 11” poster that contains the following:
 A GREAT title
 A picture of the fountain from a distance not turned on.
 A picture of the fountain turned on (showing the parabolic curve) – label the vertex and one other
point with the coordinates.
 A screen shot of the parabola equation from the graphing calculator.
 A combined shot of the parabola superimposed over the water fountain.
 The typed equation of the parabola in standard vertex form, standard form, and root form.
 Projects may be mounted onto construction or decorative paper
Back of poster:
 Your name(s)
 Water fountain number and location
Work attached:
 Steps 2,3,4,5,6 from above. (show scrap work of each partner if working with someone)
 A list indicated which partner did what. It must also be signed by both individuals.
Make the posters creative, unique and exciting to look at. Failure to type the equations will result in -10
points. They will be graded on creativity and accuracy. They will be laminated and posted at the water
fountains!
Ways to get the screen shot of your parabola:
1) Borrow silver cable from Mr. Fisher for one night only. Download TI-Connect software and then
copy/save picture by following the instructions in #2
2) Bring flash drive; turn on calculator; graph parabola with appropriate graphing window. Connect
calculator to USB port with silver cable; open TI-Connect; Click on “TI Screen Capture.” Save file.
Ways to get the superimposed picture of the calculator graph onto the water fountain.
In Powerpoint, format the picture, look for color, and look for “Set Transparent color”