Algebra II Learning Quizzes: Master Quadratic Equations, Functions, and Matrices

Question 1

Identify the type of function represented by the equation y = 2x^2 - 5x + 3 and its key characteristic.

Accepted Answer

Quadratic function; vertex (3/4, -1/4)

Answer

Linear function; y-intercept (0, 3)

Answer

Exponential function; base 2

Answer

Rational function; vertical asymptote x = 5/2

Question 2

What is the general shape of the graph of the exponential function f(x) = 2^x?

Accepted Answer

A curve that increases rapidly as x increases

Answer

A straight line with a positive slope

Answer

A parabola opening upwards

Answer

A curve that decreases rapidly as x increases

Question 3

In a quadratic equation ($ax^2 + bx + c = 0$), what does the discriminant ($b^2 - 4ac$) tell us about the equation?

Accepted Answer

The number of real solutions it has.

Answer

The sum of its two roots.

Answer

The slope of its graph.

Answer

It has no significance in analyzing quadratic equations.

Question 4

In a two-dimensional coordinate plane, vectors are represented as objects with both magnitude and direction. Which of the following operations is not applicable to vectors?

Accepted Answer

Vector division

Answer

Vector addition

Answer

Scalar multiplication

Answer

Vector subtraction

Question 5

Given f(x) = 2x - 5 and g(x) = x^2 + 1, what is (f o g)(x)?

Accepted Answer

4x^2 - 10x - 5

Answer

2x^2 - 9

Answer

2x^2 + 10x - 5

Answer

4x^2 + 5

Question 6

In the quadratic equation x^2 - 5x + 6 = 0, the solutions are:

Accepted Answer

x = 2 or x = 3

Answer

x = 1 or x = 6

Answer

x = -2 or x = -3

Answer

x = -1 or x = -6

Question 7

Find the domain and range of the function: f(x) = sqrt(x - 3)

Accepted Answer

Domain: [3, ∞), Range: [0, ∞)

Answer

Domain: (-∞, 3], Range: (0, ∞)

Answer

Domain: [-3, ∞), Range: [0, ∞)

Answer

Domain: (-∞, -3], Range: (0, ∞)

Question 8

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

Accepted Answer

(x = 2, y = 3)

Answer

(x = 3, y = 2)

Answer

(x = -2, y = -3)

Answer

(x = -3, y = -2)

Question 9

What are the coordinates of the vertex of the parabola represented by the equation y = x^2 - 4x + 3?

Accepted Answer

(1, -2)

Answer

(2, -3)

Answer

(3, -4)

Answer

(4, -5)

Question 10

What are the solutions to 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 11

What is the equation of the line passing through the points (2, 3) and (-1, 5)?

Accepted Answer

y = -2x + 7

Answer

y = 2x + 1

Answer

y = -1/2x + 4

Answer

y = 1/2x + 2

Question 12

What is the inverse of the function f(x) = 2x - 1?

Accepted Answer

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

Answer

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

Answer

f^-1(x) = 2x + 1

Answer

f^-1(x) = -2x + 1

Question 13

What is the solution to the system of equations 
 x + y = 5 
 x - y = 1?

Accepted Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 14

The factored form of the quadratic equation x^2 - 5x + 6 is:

Accepted Answer

(x - 2)(x - 3)

Answer

(x + 2)(x - 3)

Answer

(x - 1)(x - 6)

Answer

(x + 1)(x - 6)

Question 15

The vertex of the parabola y = x^2 + 4x + 3 is:

Accepted Answer

(2, 3)

Answer

(-2, 3)

Answer

(3, 2)

Answer

(-3, 2)

Question 16

The determinant of the matrix B = [[4, -2], [3, 1]] is:

Accepted Answer

10

Answer

2

Answer

6

Answer

12

Question 17

The graph of the inequality y > 2x - 1 is:

Accepted Answer

The region above the line y = 2x - 1

Answer

The region below the line y = 2x - 1

Answer

The region to the left of the line y = 2x - 1

Answer

The region to the right of the line y = 2x - 1

Question 18

A company uses a 3x3 matrix to represent sales data over four quarters. How can matrix operations be used to determine the total sales for each product and the total sales for each quarter?

Accepted Answer

Sum the elements in each row to find the total sales for each product.

Accepted Answer

Sum the elements in each column to find the total sales for each quarter.

Answer

Multiply each row by the corresponding column to find the total sales for each product in each quarter.

Question 19

What are the coordinates of the vertex of the parabola represented by the equation ?(?) = −2(? + 1)^2 + 3?

Accepted Answer

(-1, 3)

Answer

(-1, 5)

Answer

(1, 5)

Answer

(1, 3)

Question 20

What is the domain of the function ?(?) = √(? − 2)?

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

All real numbers

Question 21

Determine the domain and range of the function: f(x) = √(x - 2).

Accepted Answer

Domain: [2, ∞); Range: [0, ∞).

Answer

Domain: (-∞, 2); Range: (0, ∞).

Answer

Domain: [2, ∞); Range: (-∞, 0).

Answer

Domain: (-∞, 2); Range: (-∞, 0).

Question 22

Simplify the expression: (2 + 3i) - (4 - 5i).

Accepted Answer

-2 + 8i.

Answer

2 - 8i.

Answer

-2 - 8i.

Answer

2 + 8i.

Question 23

Determine if the following statement is true or false:
The graph of the function y = |x| is symmetric about the x-axis.

Accepted Answer

True.

Answer

False.

Question 24

Which of the following represents the graph of the quadratic function f(x) = -x² + 4x - 3?

Accepted Answer

Parabola opening downwards, vertex at (2, 1)

Answer

Circle with center (2, 1) and radius 1

Answer

Parabola opening upwards, vertex at (2, 1)

Answer

Straight line with slope -1 and y-intercept 3

Question 25

Find the determinant of the matrix: | 2 3 | | 1 4 |

Accepted Answer

5

Answer

-5

Answer

10

Answer

8

Question 26

Write the equation of the circle with center at (2, 3) and radius 5.

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x - 2)² + (y - 3)² = 5

Answer

(x + 2)² + (y + 3)² = 5

Answer

(x - 3)² + (y - 2)² = 25

Question 27

Which of the following is an equation of a line parallel to y = 2x + 1?

Accepted Answer

y = 2x + b, where b is any real number

Answer

y = x + 2

Answer

y = 2x - 1

Answer

y = -2x + 1

Question 28

Find the solutions to the equation: (x - 2)(x + 5) = 0.

Accepted Answer

x = 2, x = -5

Answer

x = 2, x = -6

Answer

x = -2, x = -5

Answer

x = -2, x = 5

Question 29

Given f(x) = 2x + 1 and g(x) = x² - 3, calculate f(g(2)).

Accepted Answer

5

Answer

3

Answer

7

Answer

-1

Question 30

Find the domain of the function: f(x) = √(x - 5).

Accepted Answer

[5, ∞)

Answer

(-∞, 5]

Answer

(-5, ∞)

Answer

(-∞, -5]

Question 31

Solve the quadratic equation by factoring: x² + 2x - 15 = 0.

Accepted Answer

x = 3 or x = -5

Answer

x = 1 or x = -15

Answer

x = 4 or x = -3

Answer

x = 2 or x = -7

Question 32

Calculate the slope of the line that passes through the points (1, 3) and (3, 9).

Accepted Answer

3

Answer

2

Answer

4

Answer

-3

Question 33

Simplify the expression: (x^2 + y^2)^2

Accepted Answer

x^4 + 2x^2y^2 + y^4

Answer

(x + y)^4

Answer

(x - y)^4

Answer

x^4 - 2x^2y^2 + y^4

Question 34

Calculate the determinant of the matrix: |2 1| |-1 3|

Accepted Answer

7

Answer

9

Answer

5

Answer

-1

Question 35

Simplify the radical expression: sqrt(80) + sqrt(20)

Accepted Answer

4sqrt(5)

Answer

2sqrt(20)

Answer

8sqrt(10)

Answer

10sqrt(2)

Question 36

Find the inverse function of f(x) = 3x + 1

Accepted Answer

g(x) = (x - 1)/3

Answer

g(x) = 3x - 1

Answer

g(x) = -3x + 1

Answer

g(x) = 1/3x + 1

Question 37

Which type of graph represents the inequality: y ≤ x^2 - 1?

Accepted Answer

A parabola opening upwards and solid on the parabola.

Answer

A parabola opening upwards and dashed on the parabola.

Answer

A parabola opening downwards and solid on the parabola.

Question 38

What is the domain of the logarithmic function: f(x) = log2(x + 3)?

Accepted Answer

x > -3

Answer

x ≤ -3

Answer

x < -3

Answer

x ≥ -3

Question 39

Factor the quadratic expression: x² - 5x + 6

Accepted Answer

(x - 3)(x - 2)

Answer

(x + 3)(x + 2)

Answer

(x + 6)(x - 1)

Answer

(x - 6)(x + 1)

Question 40

Find the x-coordinate of the vertex of the parabola defined by the function: f(x) = 2x² - 8x + 3

Accepted Answer

2

Answer

0

Answer

-4

Answer

4

Question 41

Identify the property that describes the relationship between multiplication and division:

Accepted Answer

Inverse operations

Answer

Associative property

Answer

Commutative property

Answer

Distributive property

Question 42

Simplify the algebraic expression: (3x - 2)(x + 1)

Accepted Answer

3x² - x - 2

Answer

-3x² - x - 2

Answer

3x² + x - 2

Answer

-3x² + x - 2

Question 43

Determine the number of solutions to the following equation: x² - 4x + 4 = 0

Accepted Answer

1

Answer

2

Answer

3

Answer

0

Question 44

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

Accepted Answer

f⁻¹(x) = (x - 5) / 2

Answer

f⁻¹(x) does not exist

Answer

f⁻¹(x) = 5 - 2x

Answer

f⁻¹(x) = 2x - 5

Question 45

Which of the following is the vertex of the parabola y = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(2, 1)

Answer

(-1, 2)

Answer

(1, 2)

Question 46

What is the domain of the function f(x) = 1/(x-2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

x < 2

Answer

x > 2