TEST 13 REVIEW
Quadratics
1) Solve the quadratic equation Y=5x*+3 where *=2
A. x = √(Y-3)
B. x = √(3+Y)
C. x = √(3+Y)2
D. x = (Y-3)2
2) Explain in complete sentences how to solve the following equation using the factoring method.
Y=7x+14.
3) Find the domain and range
Domain:
Range:
A)1 B) 2 C) x times itself D) Y times itself
4) Find the Axis of Symmetry on the graph below.
A)
B)
C)
D)
1
-5
-1
3
1.
2. Solve Quadratic Equation
10
9
8
7
6
5
4
3
2
1
-1
5x + 9x = -4
1 2 3 4 5 6 7 8
Graph this quadratic equation
2
y = 2x - 16x +33
3. Solve Quadratic Problem
You are trying to dunk a basketball. You need to
jump 2.5 ft. in the air to dunk the ball. The height
that your feet are above the ground in given by
the function h(t)=16t +12t. What’s the maximum
height your feet will be above the ground?
4.
Fill in this table
y=½(x–4) -2
X
Y
1. Where are the zeros located on the graph below.
A.
B.
C.
D.
(2,0) (-2,0)
(0,2) (0,-2)
(2,0) (0,-2)
(-3,0) (2,0)
2. What type of graph would the table below represent?
X 0 1 2 3 4 5
Y 0 3 6 9 12 15
A. Quadratic
B. Linear
C. None of the above
3.
I. X2
II. 3X2
III. 1/2X2
IIII. 4X2
List these equations from narrowest to widest.
A. III,I,II,IIII
B. I,III,II,IIII
C. III,I,II,IIII
D. IIII,I,II,III
4. A car is traveling at a constant speed, after 3 hours the car has traveled 180 miles. If the
car keeps moving at the same speed, how much more hours will it take for the car to
travel 270 miles?
A. 1 more hour
B. 3 more hours
C. 1 ½ more hours
D. 2 more hours
X
Y
-2
-7
-1
-3
0
?
1
5
2
9
The data in the table shows ordered pair solutions to a linear function. Find the missing y-value. show your work.
1. While on vacation in Italy, Rudy visited the Leaning Tower of Pisa. When he leaned over the railing to
look down from the tower, his sunglasses fell off. The height in meters of the sunglasses as they fell can
be approximated by the function y= -5x62+50, where ‘x’ is the time in seconds. How long did it take for
the glasses to reach the ground
2. Find the vertex of the parabola.
3. Is this function quadratic?
4. Graph the quadratic function below.
Y=4x2
1. Mathew is working on an equation f(x)=-x2 -4 if he translated by 3 units down which is the most reasonable answer
a. Y = -x2-1
b. Y = 1/3x2 - 4
c. Y = -4x2 - 4
d. Y = –x2- 7
2. Graph the following equation: f(x) = 2x2 - 6 and select the zeros of this equation.
a. (2 and 2)
b. (3 and 0)
c. (2 and 4)
d.( 2 and -3 )
3. Find the zeros on the table
x
y
Is this a quadratic function? Explain your reasoning.________________________
_________________________________________________________________________
_________________________________________________________________________
4. Which term best fits the equation 2x2 -x-15
a. (x-4)(2x+5)
b. (x+3)(2x + 5)
c.(x-3)(2x + 5)
1. How does a quadratic equation look when graphed?
a. it’s a straight line
c. it’s only one fixed point
b. like a parabola
d. there’s two curved lines that never meet
2. (ax2 + bx + c) is:
a. a quadratic formula
c. not able to be graphed
b. a parabola
d. a and b
e. always in all four quadrants when graphed
3. In the quadratic formula x =
a. always a vertex
c. an intercept
b. a solution
d. a zero
4. Use the factoring method(GCF)to solve for 3x2 + 6x + 3
1. Between what two numbers will the graph of this equation meet the y-axis? y=⅓(x+2) +6
a) Between 5 and 6
b) Between 6 and 7
c) Between 7 and 8
d) Between 8 and 9
2
2. Which of the following has no solutions?
a) x -x+1=0
b)x -x-1=0
c)x -x-2=0
d)x -x-3=0
2
2
2
2
3. James kicked a field goal, and wants to figure out how high the ball went in the air. If the path of the
football can be represented by -x -x+35 , how high did he kick the ball?
a) 4 ft
b) 10 ft
c) 35 ft
d) 20 ft
2
4. Why is this not a quadratic relationship?
a) Because the value at zero is three.
b) Because X increases at a constant rate.
c) Because Y increases at a constant rate.
d) Because the graph of the equations is a parabola.
x
y
1
3
2
5
3
7
4
9
5
11
KEY:
1C
2A
3C
4C
1. Drae, Ethan, and Matthew went to summer camp and rented a canoe. The cost of
renting a canoe is modeled by Y = X2 + 3. When Y represents the total cost, X represents
the number of hourss rented, and 3 is the one-time cost of entering the store. What is
the cost of renting the canoe for three hours?
A. $105
C. 3%of entrance fee
B. $12
D. $9
2. What is the solution for Y = 0?
3. Which graph models the equation Y = X2 + 12?
A.
B.
Y
0
1
2
X
12
13
15
B.
Y
0
1
2
Y
0
1
2
X
12
13
16
D.
X
1
2
4
4. How many solutions are in the equation y = x2
Y
0
1
2
X
1000
3121
BLANK
The height of a diver above the water during a dive can be modeled by h=-16t^2 +8t+48, where h is
height in feet and t is time in seconds. Find the time it takes for the diver to reach the water.
A. t= 3/2x
B. t=2/3x
C. t= 5/4x
D. t= 4/5
What is the line of symmetry of the polynomial above?
A. 4
B.7
C.-2
D.2
x
Y
-3
22
-2
11
-1
4
0
2
1
4
2
11
What is the vertex of the quadratic to the left?
A. 11
B. -2
C. 4
D. 2
Graph the following equation.
Y=5x^2+2
KEY:
1A
2D
3D
1. What is the parent function of the equation y=4x2-6x+7?
a.
b.
c.
d.
y=-x
y=x2
y=x2+7
y=x+7
2. The area of a new playground is 4x2+4x. Find the dimensions (length and width) by factoring. Explain
how you got your answer. MUST SHOW ALL WORK!
Length:
Width:
3. Use the tables below and decide which is a quadratic function.
a.
b.
c.
4. (x+2) (x+1) If that is the factoring of a quadratic equation, then which graph matches the factor?
a.
c.
b.
Assessment Key
1. B
2. length: 4x width: x+1
3. C
4. A
1.The Area of a rectangle is 4x^2-9. What is the perimeter?
A.8x
B.8x+12
C.4x
D.4x+6
2.A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What
will be the dimensions of the enlargement?
A.12 by 15
C.-12 by 16
B.12 by 16
D.13 by 15
3.Which equation represents the quadratic that is graphed below?
A.y=x(x-2)
B.y=x(x-2)
C.y=-x(x-2)
D.y=-x(x+2)
4.Complete the table for the graph above
-2
8
-1
3
0
1
-1
2
3
3
4
8
1) (x+1) (x-3)=0.
2) x^2 + x -4 =0.
3) x^2 -3x -4=0.
4) x^2 -4=0
Answer:
Answer:
Answer:
Answer:
X=-1, 3
X= -1+- square root 17 divided by two
X=-1, 4
X=+-2
1. A ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft. / s. Use the
formula h(t) = -16 + vt + s to find how long it will take for the ball to hit the ground.
2. Graph the following quadratic equation
y = 3x^2 + x + 1
What is the y - intercept ?
A. (0,-1)
B. (-1,0)
C. (-.5,0)
D. (.5,0)
3. Y = 2x + 5
X
1
2
3
Y
(x,y)
4. Solve x^2 + 5x + 6 = 0
1.
What are the solutions to X2+8X =-15
a) a). x=3 and x=5
b) b). x=-15 and x=-3
c) c). x=-3 and x=-5
d) d). x=9 and x=-5
2.
Which equation matches the table?
a) A). 4x2 +8x+1
b) B).5x2 +8x+7
c) C).8x2 +4x+1
d) D).9x2 +7x+2
x
y
-4
33
-3
13
-2
1
-1
-3
0
1
1
13
2
33
3
61
4
97
3.
What are the zeros of this parabola?
a) A). -6 and 1
b) B). 8 and -5
c) C). -8 and 1
d) D). 4 and 9
4.
The height of a diver above the water during a dive can be modeled by H = -16t2 + 8t + 48,
where H is height in feet and t is time in seconds. Find the time it takes for the diver to
reach the water. Write your answer in a complete sentence.
Question 1: C
Question 2: A
Question 3: C
Question 4: Its takes the diver 2 seconds.