Master Quadratic Equations: Online Quizzes and Practice

Question 1

Solve the quadratic equation: x² + 6x - 7 = 0 by completing the square.

Accepted Answer

x = -3 ± √10

Answer

x = 3 ± √10

Answer

x = -3 ± √7

Answer

x = 3 ± √7

Question 2

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

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = 2

Answer

x = 2, y = 3

Question 3

The quadratic formula used to solve quadratic equations is:

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a

Answer

x = (-b ± √(b² + 4ac)) / 2a

Answer

x = (b ± √(b² - 4ac)) / 2a

Answer

x = (b ± √(b² + 4ac)) / 2b

Question 4

In a quadratic equation, the discriminant is:

Accepted Answer

The value under the square root sign in the quadratic formula

Answer

The value of 'a' in the quadratic equation

Answer

The difference between the two roots of the equation

Answer

The sum of the two roots of the equation

Question 5

When using the quadratic formula to solve a quadratic equation, which of the following is NOT a condition?

Accepted Answer

The equation must have no real roots

Answer

The equation must be in standard form

Answer

The discriminant must be positive

Answer

The equation must have two real roots

Question 6

For the parabola represented by the quadratic equation y = x² - 4x + 3, the axis of symmetry is:

Accepted Answer

x = 2

Answer

y = 2

Answer

x = -2

Answer

y = -2

Question 7

The graph of the quadratic equation y = -x² + 4x - 3 is:

Accepted Answer

A parabola that opens downward

Answer

A parabola that opens upward

Answer

A line

Answer

A circle

Question 8

Solve the following quadratic equation: x² + 5x + 6 = 0

Accepted Answer

x = -3, -2

Answer

x = -2, -3

Answer

x = 2, 3

Answer

x = 3, 2

Question 9

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

Accepted Answer

(2, -1)

Answer

(2, -5)

Answer

(-2, 5)

Answer

(-2, -1)

Question 10

Determine the number of real solutions of the quadratic equation x² + 2x + 5 = 0

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 11

Which of the following equations is a quadratic equation?

Accepted Answer

x^2 + 2x + 1 = 0

Answer

x + y = 2

Answer

sinx = 1

Answer

1/x = 3

Question 12

Use the quadratic formula to solve the equation 2x^2 - 3x + 1 = 0.

Accepted Answer

x = -1/2, x = -1

Answer

x = 1/2, x = 1

Answer

x = 1/4, x = 1/2

Answer

x = -1/4, x = -1/2

Question 13

Which method can be used to solve a quadratic equation with complex roots?

Accepted Answer

Quadratic formula

Answer

Factoring

Answer

Completing the square

Answer

Graphing

Question 14

Find the discriminant of the quadratic equation 3x^2 - 5x + 2 = 0.

Accepted Answer

7

Answer

-7

Answer

1

Answer

-1

Question 15

Which of the following represents the vertex of the parabola y = x^2 - 2x + 1?

Accepted Answer

(1, 1)

Answer

(1, 0)

Answer

(0, 1)

Answer

(-1, 1)

Question 16

Find the axis of symmetry of the parabola y = -2x^2 + 4x - 3.

Accepted Answer

x = -1

Answer

x = 0

Answer

x = 1

Answer

x = 2

Question 17

What is the discriminant of a quadratic equation?

Accepted Answer

The expression b² - 4ac

Answer

The value of 2a

Answer

The term -b

Answer

The constant c

Question 18

What is the vertex of the parabola represented by the equation y = ax² + bx + c?

Accepted Answer

(-b/2a, c)

Answer

(b/2a, c)

Answer

(a/2b, c)

Answer

(-c/2a, b)

Question 19

Which method transforms a quadratic equation into the form (x - h)² + k?

Accepted Answer

Completing the square

Answer

Factoring

Answer

Using the quadratic formula

Answer

Graphing

Question 20

What is the axis of symmetry of a parabola?

Accepted Answer

The vertical line passing through the vertex

Answer

The horizontal line passing through the vertex

Answer

The line connecting the two x-intercepts

Answer

The line perpendicular to the x-axis

Question 21

Which method is NOT used to solve quadratic equations?

Accepted Answer

Graphing

Answer

Factoring

Answer

Completing the square

Answer

Using the quadratic formula

Question 22

Solve the quadratic equation: x² - 6x + 8 = 0

Accepted Answer

x = 2 or x = 4

Answer

x = -2 or x = -4

Answer

x = 1 or x = 8

Answer

x = -1 or x = -8

Question 23

Which of the following inequalities represents the solution set of the quadratic equation x² - 4x + 3 < 0?

Accepted Answer

x < 1 or x > 3

Answer

x < 3 or x > 1

Answer

1 < x < 3

Answer

x > 1 or x < 3

Question 24

A quadratic equation has roots at x = -3 and x = 4. What is the equation of the quadratic?

Accepted Answer

x² - x - 12 = 0

Answer

x² + x - 12 = 0

Answer

x² - x + 12 = 0

Answer

x² + x + 12 = 0

Question 25

What is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

ax + bx + c = 0

Answer

a(x + b) + c = 0

Answer

a(x^2 + bx + c) = 0

Question 26

What is the discriminant of the quadratic equation ax^2 + bx + c = 0?

Accepted Answer

b^2 - 4ac

Answer

b - 4ac

Answer

b - 2ac

Answer

b^2 + 4ac

Question 27

What type of solution does a quadratic equation have if the discriminant is positive?

Accepted Answer

Two distinct real solutions

Answer

Two complex conjugate solutions

Answer

One real solution

Answer

No real solutions

Question 28

Which of the following transformations will shift the graph of the parabola y = x^2 to the right by 3 units?

Accepted Answer

y = (x + 3)^2

Answer

y = (x - 3)^2

Answer

y = x^2 - 3

Answer

y = x^2 + 3