1. D.E.V. Project
Created by:
Tyler Fassezke

2. Problem One
• A landscaper has a job to lay a basketball
court, the length of the court is 1.75X of
the width. The man employing him will
only pay $4500 and wants the court as
large as possible. Lastly a square foot of
cement cost $2.25 with a $300 initial cost.
What is the largest he can make the
court?

3. Step one, draw it out.
1.75X
X X
1.75X

4. Step two, find the amount of square
feet possible.
1.75X
1. $4500 = $2.25X + 300
X X
-300 -300
1.75X 2. $4200 = $2.25x
divide by 2.25
3. X = 1866.66 Square Feet.

5. Step 3, solve the equation.
• 1866.66 ft.²= X Multiplied by 1.75X
• Divide both sides by 1.75
• 1066.66 = X²
• √1066.66 = √X²
• 32.66 = X

6. Last Step! Insert X into the picture.
57.15 Feet.
1.75X
32.66 32.66
X X X = 32.66 Feet Feet. Feet.
1.75X 57.15 Feet

7. Problem Two
• Simplify the following:
• 5 + 3X+12 2X³+20x²-48X
(X-1) 2X-4 X² +9X+20

8. Step One, Start with the
multiplication
3X+12 2X³+20x²-48X
2X-4 X² +9X+20
• Order of operations says multiply first.
• Next, factor the numerators and
denominators.

9. Step Two, Factor.
3X+12 2X³+20x²-48X
2X-4 X² +9X+20
3(X+4) 2X(X²+10x²-24)
2(X-2) X² +9X+20 Factor out greatest
common factor.
3(X+4) 2X(X+12)(X-2)
2(X-2) (X+5)(X+4) Factor again until you can
do no more.

10. Step Three, Simplify the
multiplication.
3(X+4) 2X(X+12)(X-2) The (X-2) on the top
2(X-2) and bottom cancel out.
(X+5)(X+4)
3(X+4) 2X(X+12) The (X+4) on the top
2 (X+5)(X+4) and bottom cancel out.
3 2X(X+12)
The 2 on the out side of
2 (X+5) the parenthesis on the
top and bottom cancel
out but the X stays.

11. Step Four, Combine the two
fractions.
3 X(X+12)
(X+5)
3X(X+12)
(X+5)

12. Step Five, Bring back the addition.
5 + 3X²+36X
X-1 (X+5)

13. Step Six, make denominator the
same so that you can add the
fractions
(x+5) 5 + 3X²+36X (X-1)
(X+5) X-1 (X+5) (X-1)

14. Step Seven, multiply the nominator.
(X+5)5 + (3X²+36X)(X-1)
(X+5)(X-1) (X+5)(X-1)
5X+25 + 3X³-3X²+36X²-36x F.O.I.L. to multiply the
fractions.
(X+5)(X-1) (X+5)(X-1)
5X+25 + 3X³+33X²-36X Combine like terms.
(X+5)(X-1) (X+5)(X-1)

15. Step Eight, Combine the fractions.
5X+25 + 3X³+33X²-36X
(X+5)(X-1) (X+5)(X-1)
3X³+33X²-31X+25
(X+5)(X-1)

16. Problem Three, Complete the
Square.
5X²+15X+24=17

17. Step One, Subtract “C” from both
sides.
5X²+15X+24=17
-24 -24
5X²+15X=-7

18. Step Two, factor out “A”
5X²+15X=-7
5(X²+5X__C__)=-7

19. Step Three, “C”=(b/2)²
5(X²+5X__C__)=-7
5/2=2.5
2.5²=6.25=C
5(X²+5X+6.25)=-7

20. Step Four, add the new “C” to both
sides. Make sureamount
“C” by the
to multiply
factored out. In this
5(X²+5X+6.25)=-7 case Five.
+5(6.25)
5(X²+5X+6.25)=24.25

21. Step Five, factor into binomial.
5(X²+5X+6.25)=24.25 It’s always
(X + or – 1/2B)²
5(X+2.5)²=24.25

22. Step Six, Divide by “A”
5(X+2.5)²=24.25
5
(X+2.5)²=4.85

23. Step Seven, Square root both
sides.
√(X+2.5)²= √4.85
(X+2.5)=2.2

24. Step Eight, Get X alone and solve
for X.
(X+2.5)=+or-2.2
-2.5 -2.5
X= -2.5+-2.2 or -2.5--2.2
X=-4.7,-.3

25. Graph the following function.
f(x)=-(X-6)(X+7)³(X-1)²(X+5)

26. Step One, Write down the X
intercepts.
-(X-6)(X+7)³(X-1)²(X+5)
6 -7 1 -5
You are trying to find what X equals so
you must take the opposite of the number
that is in the parenthesis with it to equal
zero.

27. Step Two, find where the “bounces”
are.
-(X-6)(X+7)³(X-1)²(X+5)
6 -7 1 -5
• The graph bounces when there is a
square. We have one at (X-1)². So we
have one bounce.

28. Step Three, Calculate the number
of Powers in the problem
-(X-6)(X+7)³(X-1)²(X+5)
1 + 3 + 2 + 1
There are 7 so it is odd therefore it will not
start in the same direction as it ends.

29. Step Three, positive or negative?
The equation has a negative sign in the
front, therefore the graph will start high
and end low.

30. Step Four, Draw the Graph.
f(x)=-(X-6)(X+7)³(X-1)²(X+5)
Draw the dots and then connect them. Also the (X+7)
is cubed so you must have a curve through. I
aplogiese for the sloppyness but this is the best I
could do in micro-soft powerpoint.