Download Unit 9 Exam – Quadratics - MATH-at

Interim Assessment 1
Name: _____________________
Date: _____________________
PART I: MULTIPLE CHOICE
A swim team member performs a dive from a 14-foot-high springboard. The parabola below
shows the path of her dive.
1.
Which equation represents the axis of symmetry?
(1) x = 3
(3) x = 23
(2) y = 3
(4) y = 23
What are the vertex and the axis of symmetry of the parabola shown in the diagram below?
2.
(1) The vertex is (-2,-3), and the axis of symmetry is x = -2.
(2) The vertex is (-2,-3), and the axis of symmetry is y = -2.
(3) The vertex is (-3,-2), and the axis of symmetry is y = -2.
(4) The vertex is (-3,-2), and the axis of symmetry is x = -2.
Which equation represents the axis of symmetry of the parabola below?
3.
(1) y = -3
(2) x = -25
(3) x = -3
(4) y = -25
What are the vertex and axis of symmetry of the parabola y  x2  16x  63?
4.
(1) vertex: (8,-l); axis of symmetry: x = 8
(2) vertex: (8,1); axis of symmetry: x = 8
(3) vertex: (-8,-1); axis of symmetry: x = -8
(4) vertex: (-8,1); axis of symmetry: x = -8
What is the turning point, or vertex, of the parabola whose equation is y = 3x2 + 6x -1?
(1)(-3,8)
(3)(-l,-4)
(2) (1,8)
(4) (3,44)
5.
What is the minimum point of the graph of the equation y
(1)(2,17)
(3)(-2, 1)
(2) (-2,-15)
(4) (2,33)
x2
x
6.
What are the roots of the equation x2  7 x  6  0
(1) 1 and 7
(2) -1 and 7
(3) -1 and -6
(4) 1 and 6
7.
What are the roots of the equation x 2  3x  18  0 ?
(1) 3 and 6
(2) -3 and -6
(3) -3 and 6
(4) 3 and -6
8.
What are the roots of the equation x2 + 7x + 10?
(1) 5 and -2
(2) -5 and 2
(3) -5 and -2
(4) 5 and 2
9.
10.
The length of a rectangular room is 7 less than three times the width, w, of the room. Which
expression represents the area of the room?
(1) 3w  4
(3) 3w2  4w
(2) 3w  7
(4) 3w2  7w
A rectangle has an area of 24 square units. The width is 5 units less than the length. What is
the length, in units, of the rectangle?
(1) 6
(3) 3
(2) 8
(4) 19
11.
What are the roots of the parabola shown below?
12.
(1) -2 and 2
(2) 2 and 0
(3) -4 and 0
(4) 3 and 4
What are the roots of the parabola shown below?
13.
(1) -5 and 3
(2) 5 and 3
(3) -5 and -3
(4) 5 and -3
14.
15.
16.
17.
18.
19.
20.
What is the product of x + 3 and x + 5?
(1) x2 + 15
(3) x2 – 15x + 15
(2) x2 + 2x + 15
(4) x2 + 8x + 15
What is the product of x + 7 and x + 6?
(1) x2 + 42
(3) x2 – x + 42
2
(2) x + 13x + 42
(4) x2 + x + 42
What is the product of x + 4 and x – 2?
(1) x2 – 8
(3) x2 – 2x + 8
2
(2) x + 2x – 8
(4) x2 + 6x – 8
Which expression is equivalent to (x – 6)2?
(1) x2 – 36
(3) x2 – 12x + 36
(2) x2 + 36
(4) x2 + 12x + 36
What are the factors of x2 – 16?
(1) (x – 4)(x – 4)
(2) (x + 4)(x – 4)
(3) (x – 8)(x – 8)
(4) (x + 8)(x – 8)
Factored completely, what is 25x2 – 36y2 equal to?
(1) (5x + 6y)(5x + 6y)
(3) (5x + 18y)(5x – 18y)
(2) (5x + 6y)(5x – 6y)
(4) (5x – 6y)(5x – 6y)
Factored, the expression 81a2b2 – 64a2b2 is equivalent to
(1) (9a – 8b)(9a + 8b)
(3) (9a – 32b)(9a + 32b)
(2) (9a – 8b) (9a – 8b)
(4) (9a – 32b)(9a – 32b)
21.
22.
23.
24.
What are the factors of x2 + 7x + 6?
(1) (x – 6)(x – 1)
(3) (x – 6)(x + 1)
(2) (x + 6)(x – 1)
(4) (x + 6)(x + 1)
What are the factors of x2 + 2x – 24?
(3) (x – 6)(x – 4)
(3) (x – 6)(x + 4)
(4) (x + 6)(x – 4)
(4) (x + 8)(x + 3)
Factored completely, the expression x3 + 4x2 – 12x is equivalent to
(1) x(x - 6)(x + 2)
(3) x(x + 3)(x + 4)
(2) x(x + 6)(x - 2)
(4) x(x - 3)(x - 4)
Factored completely, the expression 2x2 + 16x – 40 is equivalent to
(1) 2(x - 10)(x + 2)
(3) 2(x + 10)(x + 2)
(2) 2(x + 10)(x - 2)
(4) 2(x - 5)(x - 4)
PART II : FREE RESPONSE
A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of
the walkway is 15 feet more than the width. Write an equation that could be used to
determine the dimensions of the walkway. Solve this equation to find the length and width, in
feet, of the walkway.
25.
Graph the equation y  x 2  2 x  3 on the accompanying set of axes.
determine the roots of the equation x 2  2 x  3  0.
26.
Using the graph,
PART III: PREVIEW QUESTIONS (UNIT 3)
27.
28.
29.
2x(-1) =
5x + (-5x) =
x + 2x + 3x =
Solve for x: 2y + 4x = 10
30.
x = 4. What is the value of y in the equation 2y – 3x = 0?
31.
32.
Which of the following is a linear equation?
(A) 2x2 + 5x – 8 = y
(C) y = 8x + 4
(B) y = 3x3
(D) y = (x – 4)2
What is the slope of the line y = 4x + 6?
33.
At what point do lines below intersect?
34.