Master Quadratic Equations: Online Quizzes and Practice

Question 1

Determine a solution for the inequality: **x² - 4x > 0**

Accepted Answer

x < 0 or x > 4

Answer

0 < x < 4

Answer

x > 0

Answer

x < 0

Question 2

Determine the product of the roots of the quadratic equation: **x² - 7x + 12 = 0**

Accepted Answer

3

Answer

-3

Answer

12

Answer

-12

Question 3

Factor the following quadratic expression: 4x² - 12x + 9

Accepted Answer

(2x - 3)²

Answer

(2x + 3)²

Answer

(4x - 3)²

Answer

(4x + 3)²

Question 4

What are the solutions to the quadratic equation **(x - 3)^2 = 16**?

Accepted Answer

x = -1, x = 7

Answer

x = 1, x = 7

Answer

x = -1, x = -7

Answer

x = 1, x = -7

Question 5

A farmer has 100 meters of fencing to enclose a rectangular plot of land. What is the maximum area of the plot that he can enclose if the length is twice the width?

Accepted Answer

1250 square meters

Answer

625 square meters

Answer

2500 square meters

Answer

5000 square meters

Question 6

What is the discriminant of the quadratic equation ax² + bx + c = 0?

Accepted Answer

b² - 4ac

Question 7

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

Accepted Answer

(2, -1)

Answer

(4, -1)

Question 8

Which of the following values of k makes the quadratic equation x² + kx + 1 = 0 have only one real root?

Accepted Answer

k = 4

Answer

k = 1

Question 9

Factor the quadratic equation x^2 - 5x + 6 into (ax + b)(cx + d).

Accepted Answer

(x - 2)(x - 3)

Answer

(x + 2)(x + 3)

Answer

(x - 6)(x + 1)

Answer

(x + 6)(x - 1)

Question 10

The vertex of a parabola is at (2,3). Which equation represents this parabola if it opens upward?

Accepted Answer

y = (x - 2)^2 + 3

Answer

y = -(x - 2)^2 + 3

Answer

y = (x + 2)^2 - 3

Answer

y = -(x + 2)^2 - 3

Question 11

Identify the axis of symmetry of the parabola y = x^2 - 2x + 1.

Accepted Answer

x = 1

Answer

x = 0

Answer

x = 2

Answer

x = -1

Question 12

Determine the type of parabola represented by the equation y = -x^2 + 4x - 3.

Accepted Answer

Downward opening parabola

Answer

Upward opening parabola

Answer

Leftward opening parabola

Answer

Rightward opening parabola

Question 13

Which of the following is the formula for finding the solutions of the quadratic equation ax² + bx + c = 0 (a ≠ 0)?

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a

Answer

x = (-a ± √(a² - 4bc)) / 2b

Answer

x = (-c ± √(c² - 4ab)) / 2c

Answer

x = (a ± √(a² - 4bc)) / 2b

Question 14

Which of the following equations is a quadratic equation?

Accepted Answer

x² - 4x + 3 = 0

Answer

x + y = 5

Answer

x³ + 2x² - 5x = 0

Answer

2x - 5y = 10

Question 15

What is the x-intercept of the parabola y = ax² + bx + c (a ≠ 0)?

Accepted Answer

(-b ± √(b² - 4ac)) / 2a

Answer

(-a ± √(a² - 4bc)) / 2b

Answer

(-c ± √(c² - 4ab)) / 2c

Answer

(-b ± √(b² + 4ac)) / 2a

Question 16

Which of the following is NOT a method for solving quadratic equations?

Accepted Answer

Using a graphing calculator

Answer

Factoring

Answer

Completing the square

Answer

Quadratic formula

Question 17

Which of the following represents the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

ax + bx^2 + c = 0

Answer

ax^2 + c = bx

Answer

bx^2 + ax + c = 0

Question 18

Which of the following is NOT a commonly used method for solving quadratic equations?

Accepted Answer

Graphing

Answer

Factoring

Answer

Completing the square

Answer

Using the quadratic formula

Question 19

Find the sum of the roots of the quadratic equation: 2x^2 - 5x + 3 = 0

Accepted Answer

5/2

Answer

-5/2

Answer

3/2

Answer

-3/2

Question 20

What is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

ax + bx^2 + c = 0

Answer

a^2x + bc + x = 0

Answer

bx^2 + ax + c = 0

Question 21

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 22

Find the vertex of the parabola represented by the equation: y = x^2 - 4x + 3

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(-2, 1)

Answer

(2, 1)

Question 23

Determine the discriminant of the quadratic equation: 2x^2 + 5x - 3 = 0

Accepted Answer

29

Answer

1

Answer

-29

Answer

-1

Question 24

Which of the following is the equation of the axis of symmetry of the parabola: y = 2(x - 1)^2 + 3?

Accepted Answer

x = 1

Answer

y = 3

Answer

x = 2

Answer

y = 2

Question 25

Which of the following transformations would shift the graph of y = x^2 - 2x + 1 up by 3 units?

Accepted Answer

y = x^2 - 2x + 4

Answer

y = x^2 - 2x - 2

Answer

y = x^2 + 2x + 4

Answer

y = x^2 + 2x - 2

Question 26

Which of the following is a quadratic equation in factored form?

Accepted Answer

x(x + 3) = 0

Answer

x^2 + 2x + 1 = 0

Answer

2x^2 - 5x + 3 = 0

Answer

y = (x - 1)^2

Question 27

Which of the following is an application of quadratic equations?

Accepted Answer

Solving projectile motion problems

Answer

Finding the area of a rectangle

Answer

Calculating the volume of a cone

Answer

Determining the slope of a line

Question 28

To solve the quadratic equation x² - 5x + 6 = 0 using factoring, you need to find two numbers that add up to -5 and multiply to 6. Which of the following pairs of numbers satisfy these conditions?

Accepted Answer

(2, 3)

Answer

(-2, 3)

Answer

(2, -3)

Answer

(-2, -3)

Question 29

When solving quadratic equations, there are several methods you can use. Which of the following is NOT a valid method for solving quadratic equations?

Accepted Answer

Trial and error

Answer

Factoring

Answer

Completing the square

Answer

Using a graphing calculator

Question 30

In the quadratic equation ax² + bx + c = 0, what is the discriminant?

Accepted Answer

b² - 4ac

Answer

4ac - b²

Answer

2a

Answer

-b/2a

Question 31

Which of the following equations represents a parabola that opens downward?

Accepted Answer

y = -x² + 2x + 1

Answer

y = x² + 2x + 1

Answer

y = -x² - 2x + 1

Answer

y = x² - 2x + 1

Question 32

In the equation y = 2(x + 1)² - 3, what is the equation of the axis of symmetry?

Accepted Answer

x = 1

Answer

x = -1

Answer

y = 1

Answer

y = -1

Question 33

Which of the following is a real-world application of quadratic equations?

Accepted Answer

Modeling projectile motion

Answer

Calculating the area of a circle

Answer

Solving linear equations

Answer

Finding the roots of a polynomial

Question 34

What is the factored form of the quadratic equation y = a(x - b)(x - c)?

Accepted Answer

y = a(x - b)(x - c)

Answer

y = a(x + b)(x + c)

Answer

y = a(x - b)(x + c)

Answer

y = a(x² - bc)

Question 35

What is the standard form of a quadratic equation?

Accepted Answer

ax² + bx + c = 0

Answer

a(1 - cos θ) = r

Answer

x² + y² = z²

Answer

y = mx + c

Question 36

Solve the quadratic equation by factoring: x² - 4x + 4 = 0

Accepted Answer

x = 2 (double root)

Answer

x = 4

Answer

x = -4

Answer

x = -2

Question 37

Which of the following is NOT a method for solving quadratic equations?

Accepted Answer

Integration

Answer

Factoring

Answer

Completing the square

Answer

Quadratic formula

Question 38

Which of the following is the standard form of a quadratic equation?

Accepted Answer

ax² + bx + c = 0, where a ≠ 0

Answer

bx² + ax + c = 0

Answer

x² + bx + ac = 0

Answer

ax + bx² + c = 0

Question 39

Which of the following is a quadratic inequality?

Accepted Answer

x^2 - 4 > 0

Answer

5x = 10

Answer

x + 2 < 0

Answer

2x^2 + 3x - 5 = 0

Question 40

Which of the following represents the graph of a quadratic equation?

Accepted Answer

A parabola

Answer

A circle

Answer

A line

Answer

An ellipse

Question 41

Which of the following equations is in the standard form for a quadratic equation?

Accepted Answer

ax² + bx + c = 0, where a ≠ 0

Answer

ax + by + c = 0

Answer

ax³ + bx² + cx + d = 0

Answer

ax + b = 0

Question 42

Which of the following is a quadratic equation?

Accepted Answer

x² - 5x + 6 = 0

Answer

2x + 3 = 0

Answer

x³ - 2x² + x - 1 = 0

Question 43

Solve the equation x² - 9 = 0 by factoring.

Accepted Answer

x = ±3

Answer

x = ±9

Answer

x = -3

Answer

x = 3

Question 44

What is the discriminant of the quadratic equation 2x² + 5x - 3 = 0?

Accepted Answer

49

Answer

-1

Answer

25

Answer

1

Question 45

How many real solutions does the quadratic equation x² + 4x + 4 = 0 have?

Accepted Answer

One

Answer

Two

Answer

No real solutions

Answer

Infinitely many

Question 46

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

Accepted Answer

x = 1 or x = 5

Answer

x = 6 or x = -1

Answer

x = -1 or x = -5

Answer

x = -6 or x = 1

Question 47

The graph of a quadratic equation is a parabola. What are the coordinates of the vertex of the parabola represented by the equation y = x² - 4x + 3?

Accepted Answer

(2, -1)

Answer

(-1, 3)

Answer

(0, 3)

Answer

(1, 0)