Algebra Quiz

1.

Select the graph of the quadratic function ƒ(x) = 4 – x2. Identify the vertex and axis of symmetry. Identify the correct graph by noting it in the space below: 1st, 2nd, 3rd, 4th, or 5th.

 

2.

Select the graph of the quadratic function ƒ(x) = x2 + 3. Identify the vertex and axis of symmetry. Identify which of the graphs listed below is the correct one: 1st, 2nd, 3rd, 4th, or 5th.

3.

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)

 

 

 

   

 

4.

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.

Multiply or find the special product: (x+4)(x+9)

   
  x2 + 13x

 

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

 

   
x2 + 13x + 9

 

     

6.

Evaluate the function 

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

 

7.

The expression 9/5 C+32 where C stands for temperature in degrees Celsius, is used to convert Celsius to Fahrenheit. If the temperature is 45 degrees Celsius, find the temperature in degrees Fahrenheit.

 

8.

If 3 is subtracted from twice a number, the result is 8 less than the number. Write an equation to solve this problem.

 

9.

Plot the points and find the slope of the line passing through the pair of points (0,6), (4,0). Identify the correct graph from the ones listed below: 1st, 2nd, 3rd, or 4th.

10.

Graphically estimate the x- and y- intercepts of the graph:

y = x3 – 9x

 

11.

Find the slope of a line that passes through the given points

(-2,1) (3,4)

 

    3/5
    5/3
    -7/5
    1/2

 

 

12.

Determine whether the lines are parallel, perpendicular, both, or neither.

 

Parallel

 

 

Perpendicular

 

 

Both

 

 

Neither

 

13.

Mike works for $12 an hour. A total of 15% of his salary is deducted for taxes and insurance. He is trying to save $700 for a new bicycle. Write an equation to help determine how many hours he must work to take home $700 if he saves all of her earnings?

 

    12h – .15 = 700
    12h + .15(12h) = 700
    h – .15(12h) = 700
    12h – .15(12h) = 700

 

 

14.

Which of the following would NOT represent a parabola in real life?

    The McDonald’s arches
    The trajectory of a ball thrown up in the air
    The cables on a suspension bridge
    A pitched roof

 

15.

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

5x-3 = 3x+5

 

True

False

 

16.

Which of the following represents the general formula of a circle?

 

    y = ax2 + bx +c
    x2 + y2 = r2
    Ax + By = C
    y = mx + b

 

 

17.

When should you use the quadratic formula?

    When a quadratic equation CANNOT be factored easily or at all
    When a quadratic equation CAN be factored easily
    When a linear equation CANNOT be factored easily or at all
    When a linear equation CAN be factored easily

 

18.

Factor the Trinomial: x2 + 14x + 45

   
(x-5)(x-9)

 

    (x+5)(x-9)
   
(x+5)(x+9)

 

   
(x-5)(x+9)

 

 

19.

Solve the following by extracting the square roots:

X^2-4=0

 

20.

In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Find the number of miles driven by each. Rachel drove ___ miles and James drove ___ miles.

 

21.

To evaluate a function, we:

    Multiply f times the given number or expression
    Substitute its variable with a given number or expression
    Multiply the variable times the given number or expression
    All of the answers are correct

 

22.

To visually determine if a graph represents a function or not, we can use:

    Vertical Line Test
    Horizontal Line Test
    Domain and Range Test
    There is no way to determine from a graph.

 

23.

The table below describes a function.

 

True

False

 

24.

Evaluate the function ƒ(x) = 6x – 5 at ƒ(1)

    2
    1
    -1
    0

25.

What is the range of a function?

 

26.

Find all real values of x such that ƒ(x) = 0. ƒ(x) = 42 – 6x

    7
    5
    9
    6
    8

 

27.

What is the domain of the function?

    The set of “x” values that will produce a “y” value
    The set of “y” values that will produce an “x” value
    All real numbers
    Impossible to be determined

 

28.

Find the zeroes of the function algebraically. Write the answer, if applicable, in fraction form. ƒ(x) = 2×2 – 3x – 20

 

29.

Find (ƒ+g)(x) ƒ(x) = x+3, g(x) = x – 3

    2x
    3x
    -2x
    2x+6

 

30.

Find (ƒ-g)(x) ƒ(x) = x + 6, g(x) = x – 6

    2x – 12
    12
    2x – 6
    2x + 12

 

31.

Find (ƒg)(x) for:

    7×3 + 6×2
    7×3 – 6×2
    7×2 – 6×3
    7×2 + 6×3

 

32.

Find ƒ ∘ g for: 

    x2
    (x – 5)2
    (x + 5)2
    x2 – 5

 

33.

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.

 

    Falls to the left, rises to the right.
    Falls to the left, falls to the right.
    Rises to the left, rises to the right.
    Rises to the left, falls to the right.
    Falls to the left.

 

 

34.

Describe the right-hand and the left-hand behavior of the graph of

 

    Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
    Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
    Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
    Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.

 

35.

Using an online calculator, sketch the graph of the function to find the zeroes of the polynomial.

 

    0,2,3
    0,2,-3
    0,-2,3
    1,2,3

 

 

36.

Any non-zero number divided by zero is:

 

37.

Select the graph of the function and determine the zeros of the polynomial: f(x) = x2(x-6). Indicate which graph below is the correct one: 1st, 2nd, 3rd, or 4th.

38.

The height, h(x), of a punted rugby ball is given by  where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point? (Hint: Examine the vertex of this quadratic function)

    28 feet
    13 feet
    18 feet
    23 feet

 

39.

The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x – 0.5×2 What expenditure for advertising will yield a maximum profit? (Hint: Examine the vertex of this quadratic function)

    40
    0.5
    230
    20

 

40.

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) = -10p2 + 130p where p is the price charged per pet (in dollars). Find the price that will yield a maximum revenue.

    $7.5
    $6.5
    $8.5
    $10.5
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