# Algebra Problems

QUESTION 1

1. Select the graph of the quadratic function ƒ(x) = 4 – x2. Identify the vertex and  axis of symmetry.

 Vertex: (0,4) Axis of symmetry: y-axis Vertex: (0,2) Axis of symmetry: y-axis Vertex: (0,5) Axis of symmetry: y-axis Vertex: (0,3) Axis of symmetry: y-axis Vertex: (0,1) Axis of symmetry: y-axis 5 points

QUESTION 2

1. Select the graph of the quadratic function ƒ(x) = x2 + 3.  Identify the vertex and axis of symmetry.

 Vertex: (0,4) Axis of symmetry: y-axis Vertex: (0,5) Axis of symmetry: y-axis Vertex: (0,1) Axis of symmetry: y-axis Vertex: (0,3) Axis of symmetry: y-axis Vertex: (0,2) Axis of symmetry: y-axis 5 points

QUESTION 3

1. Determine the vertex of the graph of the quadratic function      5 points

QUESTION 4

1. Determine the x-intercept(s) of the quadratic function

ƒ(x) = x2 + 4x – 32

 (-4,0), (8,0) (0,0), (7,0) (4,0), (-8,0) (0,0), (-7,0) no x-intercept(s)

5 points

QUESTION 5

1. Write a polynomial that fits the description.

A fifth-degree polynomial with leading coefficient 4

 1024×5 + 3x + 1 4×5 + 3x + 1 4×4 + 3×3 + 4×2 + 5x + 1 6×5 + 3x + 1 x5 + 4

5 points

QUESTION 6

1. Perform the operation and write the result in standard form.

(3×2 + 5) – (x2 – 4x + 5)

 3×2 + 4x 2×2 + 4x + 5 2×2 – 4x 2×2 + 4x 2×2 + 4x – 5

5 points

QUESTION 7

1. Multiply or find the special product.

(x+4)(x+9)

 x2 + 13x x2 + 4x + 36 x2 + 36 x2 + 13x + 36 x2 + 13x + 9

5 points

QUESTION 8

1. Factor out the common factor.

8×3 – 104x

 8×3(1-13x) 8(x3-13x) 8×2(x-13) x(8×2-104) 8x(x2-13)

5 points

QUESTION 9

1. Factor the Trinomial.

x2 + 14x + 45

 (x-5)(x-9) (x+5)(x-9) (x+5)(x+9) (x-5)-(x-9) (x-5)(x+9)

5 points

QUESTION 10

1. Determine whether the value of x=0 is a solution of the equation.

5x-3 = 3x+5

 yes no

5 points

QUESTION 11

1. Solve the equation and check your solution.

67x – 24 = 3x + 8(8x-3)

 3 67 -3 -67 All real numbers

5 points

QUESTION 12

1. Solve the quadratic equation by factoring.

x2 – 6x + 5 = 0

 -1,5 -1,-5 1,-5 1,5 6,5

5 points

QUESTION 13

1. Solve the equation and check your solution. (If not possible, explain why) 8 7/17 15/8 12 15

5 points

QUESTION 14

1. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.  Sketch the line.

 y=6x+6 y=6x+6 y = -6x-6 y = -2x – 6 y = 6x-6 5 points

QUESTION 15

1. Evaluate the function at q(3)

 1/8 1/6 1/4 1/7 1/5

5 points

QUESTION 16

1. Does the table describe a function? yes no

5 points

QUESTION 17

1. Find the domain of the function. All real numbers x Non-negative real numbers x such that x ≠ 0 Non-negative real numbers x All real numbers x such that x<0 All real numbers x such that x>0

5 points

QUESTION 18

1. Find the zeroes of the function algebraically.

ƒ(x) = 2×2 – 3x – 20

 -5/2, 4 -5/2, -4 -2/5, 4 5/2, -4 5/2, 4

5 points

QUESTION 19

1. Find (f+g)(x)

ƒ(x) = 2x – 4, g(x) = 6 – x

 3x – 2 2x – 2 2x + 2 3x + 2 x+2

5 points

QUESTION 20

1. Find g ∘ f

ƒ(x) = x3, g(x) = x – 1

 x3 – 1 x3 (x – 1)3 (x3 + 1) (x + 1)3
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