EOCT REVIEW
UNIT 5 Quadratic Functions
Name
Write each expression in factored form.
1.
x2-2x-15
2.
3.
- 18x + 81
4^2-25
or
Complete each square and write the resulting equation. Then solve.
5. 4^2 + 12x + 8 = 0
4.
.y=4.
solution set:
solution set:
-3
Choose the best answer.
6. A baseball was launched from a pitching
machine that was placed on a platform.
The height of the ball, in feet, is given by
the equation h = -\bt^ + 85t + 9,
where t is the time, in seconds, since the
ball was launched. What is the meaning of
the term 85t?
^
The platform was 85 feet high.
B?\e ball was launched with an initial
upward velocity of 85 feet per second.
^^i>^The ball was launched with an initial
velocity of 85 miles per hour.
The upward velocity is changing at a
rate of 85 miles per hour per second.
J- - L -'^ .
Which
of
the
following
equivalences
can
7.
be used to factor
- y^l
[ AJ difference of squares,
^
= {a +
b){a-b)
B. difference of cubes,
-b^ = {a + b){a} + ab + b^)
C. sum of cubes,
+ &3 = (a + fo)(a2 - ab + b^)
D. square of a difference,
(a - by = a^- lab + b'^
Solve each quadratic equation.
-'
8. &2 _ lofc + 2 = 98
9. 4c2 + 28c = 120
M H -- iff
10. 5/2 - 3/ = 8
I'lo,
3j
11. g''-Ag
= 7
r
-Jp
f
Determine an expression to represent the situation.
12. A penny was dropped off the top of a bridge that is 40 feet high. The height, in feet, of the penny t
seconds after begin dropped is given by the expression -ISt'^ + bt + c.
The value of b, the coefficient of t is
D
The value of c, the constant term, is
¥0
So, the expression for the height of the penny at any time t is
-/hi
-t ^0
Choose the best answer.
13. Which transformation describes how
function/was transformed to create
function^ below?
14. Which of the following is true of function
h graphed below?
y
y
.
!''!'"!
(A) g{x>,=nx + A)
B. 5 W = / ( ^ - 4 )
;
'
- <
' /
/ t
^AT It has noy-intercept.
Its axis of symmetry is y = 1.
I
It has a positive leading coefficient, a.
its vertex is at (1, 2).
t
C. 5 W = / W + 4
D. 5W = / W - 4
©
Write an equation in one variable to describe each situation. Then solve the problem.
15. The product of two consecutive odd numbers is 1,295. What are the numbers?
2^^<y fx/-^ J Equation: X^/^2l^/:^f^
Numbers:
,
^/r
Yt31-0
, •>
Y'^S
16. A rectangle's length is four more than twice its width. Its area is 160 square inches. What is its
length?
Ma^ = ^,y,
)^f2y + H)
-K^O
Equation:
Xf
j =
/6<9
Numbers:
^eng-h^ =ZOi^
2/
((^fojY'8^
Solve the system of equations algebraically. Give the solutions, if any, as ordered pairs.
17. y = x^ x-1
^ y-x = -l
-'O
fO , Q •
18. y =
+ 3x + 9 ^^1^1^fji^^ 19. y = x^ + 30x + 100
y = 5x + 2
^ 6x = y + 44
-O
The table below represents a quadratic function. Use the table for question 20.
X
m
0
8
1
11
2
20
3
35
4
56
5
83
I
lis
20. What is the average rate of change for the function on the interval [0/1]?
What is the average rate of change for the function on the interval [3, 4]?
^1
What is the average rate of change for the function on the interval [0, 4]?
/2-
21. The graph at the right represents the function / .
-iC'^^
A second function, g, is represented by the
equation g{x) = Sx^ — 3. Compare the following
^ T
key features for these two functions.
—\
Identify and compare the x- and y-intercepts,
if any. j
^
^L<a/i r'l-f-/'^ - i ^ i P ^ .^di
(1.0)
~^
i
peifr> ^Up,
Identify and compare end b e h a v i o r . ^ : ^ . A ^ * ^ ^ . ^ ^ — i — i — t — + — t -
(ho)
^^a1Ir1e^eo/i,1^cfar/='^fdorv^
^ ' r ) ^ , ^ . c ^
function has the greater value? How do you know?
\
Use the function / ( x ) = 2x^ - 2x - 144 to answer questions 22 and 23.
22. Write the function in fully factored form.
23. What are the zeros of the function?
2(y'--/:-
72.) :
zf^-
^Jfx
/Z^<<< ^
Use the information below to answer questions 24 and 25.
The height of a ball thrown from the top of a platform can be modeled by the equation
/ ( x ) = —16x2 + 64x — 34 where / ( x ) is the height of the ball, in feet, x seconds after
the ball was thrown.
/^^i^ - / ^ ( ^ X )
-3i-^^tf
24. Complete the square to write the function in vertex form.
-/(/c)- -/(^
fy-'Zl^'-f-^D
25. Find and interpret the coordinates of the vertex and the maximum of the function.
Graph the function on the coordinate plane. Then identify the intercepts and maximum or minimum for
the function.
26. / ( x ) = - ^ ( x - 2 ) 2 + 8
y-intercept(s):
(Ofb)
x-intercept(s): f' ^)
maximum:
(^/^)
,
2
minimum:
[x-zT--X—^>
27. Which of the following inequalities is
graphed below?
A.
B. y < -x^ - 3
C.
0
y>ix2-3
D) y < i x 2 - 3
28. The owner of an orange grove found that
the number of orange trees planted per
acre affected the total number of oranges
produced in that acre, as shown in the
table.
Number of
Number of trees, x
oranges, f(x)
20
12,960
25
14,750
30
15,840
35
16,380
40
16,320
mf4
45
15,650
50
14,400
Which of the following is the best ^ ^ ^ ^
quadratic model for these data?
^fijyL^f{x)
= 47.1x2 + 13,535x
/ f ) fix) = -47.1x2 + 13,535
C / ( x ) = - 1 2 x 2 + 887x + 35.7
D. fix) = - 1 2 x 2 _ 887x = 35.7
29. A coin was dropped from the top of a bridge that is 100 feet
high. The function that describes the coin's height, y, in feet,
X seconds after it was dropped is y = -Ibx^ + 100. A graph
of this function is shown on the right. Based on the context of
this question, what are a reasonable domain and range for
the function?
O ^ lA^
100
i O,
looj
30. A baker sells cupcakes for $3 each. Her revenue, in dollars, is modeled by the function R{x) = 3x,
where x is the number of cupcakes sold. Her costs can be modeled by the function
C{x) = 0.02x2 + 0.5x + 50, where x is the number of cupcakes she sells. The function to model
her profit, in dollars, P, can be computed by subtracting her costs from her revenue. Write an
explicit equation for P in terms of x, the number of cupcakes she sells.
-
-O-OlyL^^
-
SO
31. The height, h, in meters of a soccer ball after Sydney kicks it from the ground with an initial velocity
of 10 meters per second is modeled by the equation h = - 4 . 9 t 2 + lOt. How long will it take the
soccer ball to reach a height of 8 meters?
.i/<^-^^ .f-/^t
- ^•'^•fHUi --O^ ^
-V9
32. An electroni^SsStore discoyAs\that it can selK5\elevisions
Wnen the t^^lev^ions are.6n saNe for $100,
equation |i6 conipare the price of a televisj/on, in\dollars
qua^rati^'equation to compare V>e revenjue, m.
day by pricing them at $]
them evej!
e number so^
visior*^tothAnur
each.
-^o