Algebra Quizzes: Master Linear, Quadratic, and Polynomial Functions

Question 1

Examine the linear function y = 2x - 5. Determine its slope, y-intercept, and express it in slope-intercept form.

Accepted Answer

Slope: 2, y-intercept: -5, equation: y = 2x - 5

Answer

Slope: -5, y-intercept: 2, equation: y = -5x + 2

Answer

Slope: 1, y-intercept: -2, equation: y = x - 2

Answer

Slope: 2, y-intercept: 0, equation: y = 2x

Question 2

Factor the quadratic expression (x^2 - 9) using the difference of squares formula.

Accepted Answer

A. (x + 3)(x - 3)

Answer

B. (x^2 + 3)(x^2 - 3)

Answer

C. (x - 9)(x + 9)

Question 3

In the quadratic equation ax² + bx + c = 0, the discriminant, Δ = b² - 4ac, plays a crucial role in determining the number and nature of its roots. Explain how Δ affects the roots.

Accepted Answer

If Δ > 0, the equation has two distinct real roots.

Accepted Answer

If Δ = 0, the equation has one real root with multiplicity 2.

Accepted Answer

If Δ < 0, the equation has two complex conjugate roots.

Answer

The discriminant does not provide any information about the number or nature of the roots.

Question 4

Determine the equation of the line passing through points (2, 3) and (4, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = 2x - 1

Answer

y = x - 1

Question 5

Solve the system of equations:2x + y = 5 and x - y = 1.

Accepted Answer

(2, 1)

Answer

(1, 2)

Answer

(-1, 2)

Answer

(-2, 1)

Question 6

Which graph represents the inequality 2x + y ≤ 6?

Accepted Answer

Graph with shaded region below the line y = -2x + 6 (solid line)

Answer

Graph with shaded region above the line y = -2x + 6 (solid line)

Answer

Graph with solid line y = -2x + 6

Answer

Graph with dashed line y = -2x + 6

Question 7

Determine the vertex of the parabola represented by y = x^2 - 4x + 3

Accepted Answer

(2, 3)

Answer

(2, -5)

Answer

(4, -5)

Answer

(4, 3)

Question 8

State the domain of the function: f(x) = 1 / (x - 5)

Accepted Answer

(-∞, 5) U (5, ∞)

Answer

(-∞, ∞)

Answer

[5, ∞)

Answer

(5, ∞)

Question 9

Solve the inequality: 3(x - 2) > 2x + 5.

Accepted Answer

x > 7

Answer

x < 7

Answer

x > 11

Answer

x < 11

Question 10

Which statement about polynomial functions is NOT true?

Accepted Answer

They must have a finite number of terms.

Answer

They can be expressed as a sum of terms.

Answer

They have a constant, linear, or quadratic term.

Answer

They can have any degree.

Question 11

Solve the quadratic equation: 2x^2 - 5x + 2 = 0

Accepted Answer

x = 1, x = 2

Answer

x = -1, x = -2

Answer

x = 1/2, x = 2

Answer

x = -1/2, x = -2

Question 12

What is the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

x > 2

Answer

x < 2

Answer

x >= 2

Answer

x <= 2

Question 13

Find the roots of the polynomial x^3 - 2x^2 - 5x + 6.

Accepted Answer

-1, 2, 3

Answer

1, 2, 3

Answer

1, -2, 3

Answer

-1, -2, 3

Question 14

Which transformation will shift the graph of y = x^2 to the left by 3 units?

Accepted Answer

y = (x - 3)^2

Answer

y = (x + 3)^2

Answer

y = 3x^2

Answer

y = x^2 + 3

Question 15

Identify the domain of the rational function: f(x) = 1 / (x - 2)

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All real numbers except 0

Answer

All real numbers greater than 2

Question 16

Find the equation of the circle with its center at (2, -3) and a radius of 5.

Accepted Answer

(x - 2)² + (y + 3)² = 25

Answer

(x + 2)² + (y - 3)² = 5

Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 5

Question 17

To find the coordinates of the intersection points between a linear function f(x) and a quadratic function g(x), which method should you use?

Accepted Answer

Solve the system of equations created by setting f(x) equal to g(x).

Answer

Graph both functions and estimate the intersection points visually.

Answer

Use a calculator to find the zeros of the quadratic function.

Answer

Apply the Pythagorean theorem to the coordinates of the parabola's vertex and the linear function's x-intercepts.

Question 18

Find the vertex of the quadratic function: y = x^2 - 4x + 3

Accepted Answer

(1, -2)

Answer

(2, -1)

Answer

(3, 0)

Answer

(4, 1)

Question 19

Determine the domain of the function: f(x) = √(x-1)

Accepted Answer

x ≥ 1

Answer

x ≥ 0

Answer

x < 1

Answer

All real numbers

Question 20

Find the inverse of the function: f(x) = 2x + 5

Accepted Answer

f^(-1)(x) = (x - 5)/2

Answer

f^(-1)(x) = (x - 5)/4

Answer

f^(-1)(x) = (2x - 5)/4

Answer

f^(-1)(x) does not exist

Question 21

Which of the following is the graph of the equation y = 2x - 1?

Accepted Answer

A straight line with a slope of 2 and a y-intercept of -1

Answer

A straight line with a slope of -2 and a y-intercept of 1

Answer

A parabola with a vertex at (0, -1)

Answer

A circle with a radius of 1

Question 22

Factor the quadratic expression: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Answer

(x + 9)(x + 9)

Question 23

Solve for x: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 24

Evaluate the expression for x = 2 and y = -1: 2x^2 - 3xy + y^2

Accepted Answer

5

Answer

1

Answer

3

Answer

7

Question 25

Which of the following is the factored form of x^2 - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)^2

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Question 26

Translate the algebraic expression 2x + 5y into words

Accepted Answer

Twice a number x plus five times a number y

Answer

The difference between two times x and five divided by y

Answer

The product of two times x and five times y

Answer

The sum of two times x and five divided by y

Question 27

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 5x + 2 = 0

Answer

x^2 + y^2 = 9

Answer

2x^3 - 5x + 1 = 0

Answer

x + 2 = 5

Question 28

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 1)

Answer

(x - 2)^2

Answer

x(x - 4)

Question 29

Transform the function f(x) = x^2 by shifting it 2 units up

Accepted Answer

f(x) = x^2 + 2

Answer

f(x) = (x + 2)^2

Answer

f(x) = x^2 - 2

Answer

f(x) = (x - 2)^2

Question 30

Find the vertex of the parabola: y = -x^2 + 6x - 5

Accepted Answer

(3, 4)

Answer

(2, 3)

Answer

(3, -4)

Answer

(4, 3)

Question 31

Find the vertex of the parabola given by the equation y = x² - 4x + 3.

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(-2, 11)

Answer

(1, -1)

Question 32

The function f(x) = x² is transformed by a reflection across the x-axis and a translation 3 units to the right. Write the equation of the transformed function.

Accepted Answer

f(x) = -(x - 3)²

Answer

f(x) = (x + 3)²

Answer

f(x) = (x - 3)²

Answer

f(x) = x²(x - 3)

Question 33

Solve the quadratic equation x² - 5x + 6 = 0.

Accepted Answer

x = 2 and x = 3

Answer

x = -2 and x = -3

Answer

x = 1 and x = 6

Answer

x = -1 and x = -6

Question 34

Identify the degree of the polynomial: 3x⁴ - 2x² + 5

Accepted Answer

4

Answer

5

Answer

3

Answer

2

Question 35

Solve the linear inequality: 2x + 3 > 7

Accepted Answer

x > 2

Answer

x > -2

Answer

x < 2

Answer

x < -2

Question 36

What is the slope of the line represented by the equation 2x + 3y = 6?

Accepted Answer

-2/3

Answer

-3/2

Answer

2/3

Answer

3/2

Question 37

Which of the following is the solution to the system of equations: 2x + y = 5 and x - y = 1?

Accepted Answer

x = 2, y = 1

Answer

x = -1, y = 3

Answer

x = 1, y = 2

Answer

x = 3, y = -1

Question 38

The graph of the equation y = -2x² + 4x - 1 is a:

Accepted Answer

Parabola

Answer

Line

Answer

Circle

Answer

Hyperbola

Question 39

What are the roots of the quadratic equation x² - 5x + 6 = 0?

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = 1, x = 6

Answer

x = -1, x = -6

Question 40

If f(x) = 3x - 2, what is f(-1)?

Accepted Answer

-5

Answer

5

Answer

-1

Answer

1

Question 41

The vertex of the parabola represented by the equation y = (x + 2)² - 3 is:

Accepted Answer

(-2, -3)

Answer

(-2, 3)

Answer

(2, -3)

Answer

(2, 3)

Question 42

Which of the following is NOT a polynomial function?

Accepted Answer

y = √x + 1

Answer

y = 2x⁴ - 7

Answer

y = 5x² + 3x - 1

Answer

y = x³ - 2x² + 5

Question 43

If the equation of a line is y = 2x + 5, what is the equation of a line parallel to it that passes through the point (1, 3)?

Accepted Answer

y = 2x + 1

Answer

y = -1/2x + 7/2

Answer

y = -2x + 5

Question 44

The expression (x² - 4) / (x - 2) simplifies to:

Accepted Answer

x + 2, x ≠ 2

Answer

x - 2

Answer

x² - 2

Answer

x + 4

Question 45

A rectangle has a length of (x + 3) units and a width of (x - 2) units. What is the area of the rectangle?

Accepted Answer

x² + x - 6 square units

Answer

x² - 6 square units

Answer

2x + 1 square units

Question 46

What is the slope of the line represented by the equation 2x + 3y = 6?

Accepted Answer

-2/3

Answer

2/3

Answer

-3/2

Answer

3/2

Question 47

If f(x) = 3x - 2, what is the value of f(4)?

Accepted Answer

10

Answer

2

Answer

14

Question 48

Which of the following is the equation of a line that passes through the points (1, 2) and (3, 6)?

Accepted Answer

y = 2x

Answer

y = x - 1

Answer

y = -2x + 4

Answer

y = x + 1

Question 49

What is the vertex of the parabola represented by the equation y = x² - 4x + 3?

Accepted Answer

(2, -1)

Answer

(1, 0)

Answer

(3, 0)

Answer

(0, 3)

Question 50

Solve the following system of equations: 2x + y = 7 and x - 2y = -1

Accepted Answer

x = 3, y = 1

Answer

x = -1, y = -3

Answer

x = 2, y = 3

Answer

x = 1, y = 3

Question 51

What is the simplified form of the expression (x² - 4) / (x + 2)?

Accepted Answer

x - 2

Answer

x² - 2

Answer

x + 2

Question 52

Which of the following is a factor of the polynomial x³ - 6x² + 11x - 6?

Accepted Answer

x - 1

Answer

x - 2

Answer

x + 1

Answer

x + 2

Question 53

What is the solution set of the inequality 2x + 5 < 11?

Accepted Answer

x < 3

Answer

x > -3

Answer

x < -3

Answer

x > 3

Question 54

The graph of the function y = -2x² is a parabola. Which of the following describes the direction of the parabola?

Accepted Answer

Opens downwards

Answer

Opens to the left

Answer

Opens to the right

Answer

Opens upwards

Question 55

If the graph of the function y = f(x) is shifted 3 units to the right and 2 units down, what is the equation of the transformed function?

Accepted Answer

y = f(x - 3) - 2

Answer

y = f(x + 3) + 2

Answer

y = f(x - 3) + 2

Answer

y = f(x + 3) - 2