Name: ______Date: ______Hr: ______
POOL DECKS 1—Writing Quadratic Equations
1(a).Have everyone in your group pick a different length, x, for the side of their SQUARE pool. The choice must be at least 4 feet long or larger. Write your choice for x below, and then DRAWPOOL #1 on the attached graph paper. (Be sure to label it as POOL #1).
X = ______(MY CHOSEN POOL SIDE LENGTH. CHOOSE A LENGTH 4 FEET OR GREATER)
(b)Find the area for your pool.A = ______(MY POOL#1 AREA)
(c)Find a formula that would give the area of any pool in your group, no matter what value they have for x. Your formula should have an ‘x’ in it somewhere!!
A = ______(FORMULA FOR ANY POOL#1 AREA)
(d)Check if your formula works: Plug in your chosen x-value to your formula and see if you get the correct area. Show what you plugged in. Have your group members do the same for their x-value.
A = ______= ______(CHECK YOUR FORMULA FOR POOL #1 AREA)
2(a).Have everyone in your group keep their length, x, for the side of their SQUARE pool, but now add a 3 foot wide deck to the side of the pool as shown in pool #2. Then each person should DRAWPOOL #2 on the attached graph paper. (Be sure to label it as POOL #2).
(b)Find the area for your deck only in #2.D = ______(MY DECK #2 AREA)
Find the area for your pool only in #2.P = ______(MY POOL #2 AREA)
Find the area for your pool AND deck together in #2.A = ______(MY TOTAL #2 AREA)
(c)Find a formula that would give the area of any deck portion, any pool portion, or any total area for pool #2, no matter what value x-has. [Hint: Your total area formula should have an ‘x2’ term ADDED TO some term with an ‘x’.] Check your formulas with your teacher and your group members.
Area for any deck only in #2.D = ______(FORMULA FOR ANY DECK #2 AREA)
Area for any pool only in #2.P = ______(FORMULA FOR ANY POOL #2 AREA)
Area for any pool AND deck together in #2.A = ______(FORMULA FOR ANY TOTAL #2 AREA)
2. (continued)
(d)Check if your problem #2 formulas work: Plug in your chosen x-value to your pool #2 formulas and see if you get the correct areas. Show what you plugged in. Have your group members do the same for their x-value.
D = ______= ______(CHECK YOUR FORMULA FOR DECK #2 AREA)
P = ______= ______(CHECK YOUR FORMULA FOR POOL #2 AREA)
A = ______= ______(CHECK YOUR FORMULA FOR TOTAL #2 AREA)
3(a).Have everyone in your group keep their length, x, for the side of their SQUARE pool, and the 3 foot wide deck on the side of the pool. Now everyone should add a 2-foot by 2-foot barbeque to the deck area as shown in the picture for pool #3. Then each person should DRAWPOOL #3 on the attached graph paper. (Be sure to label it as POOL #3).
(b)Find the area for your deck only in #3.D = ______(MY DECK #3 AREA with bbq)
(include the BBQ)
Find the area for your pool only in #3.P = ______(MY POOL #3 AREA)
Find the area for your pool AND deck together in #3.A = ______(MY TOTAL #3 AREA)
(c)Find a formula that would give the area of any deck + BBQ portion, any pool portion, or any total area for situation #3, no matter what value x-has. [Hint: Your total area formula should have an ‘x2’ term ADDED TO some term with an ‘x’ added to some constant number term for the BBQ.] Check your formulas with your teacher and your group members.
Area for any deck + bbq in #3.D = ______(FORMULA FOR ANY DECK with bbq #3 AREA)
Area for any pool only in #3.P = ______(FORMULA FOR ANY POOL #3 AREA)
Area for any pool, bbq AND deck together in #3.
A = ______(FORMULA FOR ANY TOTAL #3 AREA)
(d)Check if your problem #3 formulas work: Plug in your chosen x-value to your situation #3 formulas and see if you get the correct areas. Show what you plugged in. Have your group members do the same for their x-value.
D = ______= ______(CHECK YOUR FORMULA FOR DECK with bbq #3 AREA)
P = ______= ______(CHECK YOUR FORMULA FOR POOL #3 AREA)
A = ______= ______(CHECK YOUR FORMULA FOR TOTAL #3 AREA)
4(a).Rewrite your total Area formulas for each pool below. Record the value for a, b, and c (where A = ax2 + bx + c). Then fill in the charts for the area of each pool by plugging in the number for x into each formula.
POOL #1A = ______a = ____b = ____c = ____
x (side length) / -5 / -3 / -1 / 0 / 1 / 3 / 5A (area)
POOL #2A = ______a = ____b = ____c = ____
x (side length) / -5 / -3 / -1 / 0 / 1 / 3 / 5A (area)
POOL #3A = ______a = ____b = ____c = ____
x (side length) / -5 / -3 / -1 / 0 / 1 / 3 / 5A (area)
(b)On the back of your graph paper, make a set of axes and graph Area (y-axis) vs. sidelength (x-axis). Graph the data for all 3 pools on the same set of axes. Graph each pool in different colors or symbols so they can be told apart; label which graph represents which pool.
(c)Look at the shapes of your graphs. Do they match the patterns we found on our graphing calculator and changed the a, b, and c? What would make graphing these equations easier? Explain.