Quadratic Equations and Functions: Master the Basics with Interactive Quizzes

Question 1

Determine 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 2

Which of the following represents the discriminant of the quadratic equation 2x² - 3x + 1 = 0?

Accepted Answer

7

Answer

-7

Answer

-1

Answer

1

Question 3

Construct the equation of the quadratic function with an intercept of (0, -3) and a turning point at (2, -5).

Accepted Answer

y = -(x - 2)² - 3

Answer

y = (x - 2)² - 3

Answer

y = -x² + 4x - 3

Answer

y = x² - 4x - 3

Question 4

Solve the quadratic equation using the quadratic formula: 2x² + 5x - 3 = 0

Accepted Answer

x = 3/2 or x = -1

Answer

x = -3/2 or x = 1

Answer

x = -1/2 or x = 3

Answer

x = 1/2 or x = -3

Question 5

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

Accepted Answer

9

Answer

1

Answer

25

Answer

49

Question 6

The quadratic formula is used to solve quadratic equations. Which of the following is the correct formula?

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a

Answer

x = (-b + √(b² - 4ac)) / 2a

Answer

(x + a)² = b

Answer

x² + y² = r²

Question 7

The axis of symmetry of a parabola is a vertical line passing through the turning point. Which of the following is the equation of the axis of symmetry of the parabola y = x² - 4x + 3?

Accepted Answer

x = 2

Answer

y = 2

Answer

x = -2

Answer

y = -2

Question 8

The turning point of a parabola represents its minimum or maximum value. What is the turning point of the parabola y = -x² + 6x - 5?

Accepted Answer

(3, 8)

Answer

(3, -8)

Answer

(2, 3)

Answer

(2, -3)

Question 9

The discriminant of the quadratic equation (2x^2 + 5x + 3 = 0) is:

Accepted Answer

11

Answer

-11

Question 10

Which of the following is the equation of the axis of symmetry for the graph of the function y = x^2 - 2x + 3?

Accepted Answer

x = 1

Question 11

The parabola y = -x^2 + 4x - 3 opens:

Accepted Answer

Downwards

Question 12

Which of the following equations represents a quadratic function that has no real roots?

Accepted Answer

(x^2 - 4x + 4 = 0)

Question 13

The intercepts of the graph of the quadratic function y = x^2 - 5x + 6 are:

Accepted Answer

(1, 0) and (6, 0)

Answer

(0, 6) and (6, 0)

Question 14

The equation of the quadratic function that has roots at x = 2 and x = 5 is:

Accepted Answer

y = x^2 - 7x + 10

Answer

(y = x^2 + 7x + 10)

Question 15

The quadratic function y = ax^2 + bx + c has a minimum value at x = -1. Which of the following is true about the coefficients a, b, and c?

Accepted Answer

a > 0, b < 0, c > 0

Answer

a < 0, b > 0, c > 0

Question 16

Complete the square for the quadratic expression: x² + 4x

Accepted Answer

x² + 4x + 4

Answer

x² + 4x - 4

Answer

x² - 4x + 4

Answer

x² - 4x - 4

Question 17

Solve the quadratic equation: x² + 5x - 6 = 0, using factorisation.

Accepted Answer

x = 2, x = -3

Answer

x = 1, x = -6

Answer

x = 3, x = -2

Answer

x = 4, x = -1

Question 18

Which of the following is the graph of the quadratic function (y = 2(x - 1)² + 3)?

Accepted Answer

A parabola opening upwards with vertex (1, 3)

Answer

A parabola opening downwards with vertex (1, 3)

Answer

A parabola opening upwards with vertex (-1, 3)

Answer

A parabola opening downwards with vertex (-1, 3)

Question 19

Complete the square to write the expression (2x² + 8x + 5) in the form ((x + a)² + b)

Accepted Answer

(x + 2)² + 1

Answer

(x + 2)² - 1

Answer

(x - 2)² + 1

Answer

(x - 2)² - 1

Question 20

Find the equation of the axis of symmetry of the parabola (y = 3(x - 2)² + 1)

Accepted Answer

x = 2

Answer

x = -2

Answer

y = 2

Answer

y = -2

Question 21

Which of the following is the standard form of the quadratic formula for solving the quadratic equation ax² + bx + c = 0, where a ≠ 0?

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a

Answer

x = (b ± √(b² - 4ac)) / 4a

Answer

x = (-b ± √(b² + 4ac)) / 2a

Answer

x = (b ± √(b² + 4ac)) / 2a

Question 22

Consider the equation of a quadratic function f(x) = (x - h)² + k. What is the vertex point of its graph?

Accepted Answer

(h, k)

Answer

(-h, k)

Answer

(h, -k)

Answer

(-h, -k)

Question 23

If the discriminant (b² - 4ac) of a quadratic equation is negative, what does this indicate about its solutions?

Accepted Answer

The equation has no real solutions

Answer

The equation has two distinct real solutions

Answer

The equation has two equal real solutions

Answer

The equation has one real solution

Question 24

Select the methods that can be employed to solve a quadratic equation:

Accepted Answer

Factoring, Completing the square, Quadratic formula

Answer

Integration

Answer

Differentiation

Question 25

In a quadratic equation ax² + bx + c = 0, what does the value of 'b' represent?

Accepted Answer

Coefficient of the linear term

Answer

Coefficient of the quadratic term

Answer

Coefficient of the constant term

Question 26

Determine which of the following is the quadratic equation with roots α = 3 and β = 5:

Accepted Answer

x² - 8x + 15 = 0

Answer

x² - 8x - 15 = 0

Answer

x² + 8x - 15 = 0

Answer

x² + 8x + 15 = 0

Question 27

Which of the following is the correct factored form of the quadratic equation x² - 10x + 24 = 0?

Accepted Answer

(x - 4)(x - 6) = 0

Answer

(x - 4)(x + 6) = 0

Answer

(x + 4)(x + 6) = 0

Answer

(x + 4)(x - 6) = 0

Question 28

Identify the axis of symmetry of the quadratic function y = -x^2 + 6x - 5.

Accepted Answer

x = 3

Answer

y = 3

Answer

y = -3

Answer

x = -3

Question 29

Which of the following describes the graph of the quadratic function y = 2x^2 - 4x + 1?

Accepted Answer

A parabola opening upwards with its vertex at (1, 0).

Answer

A parabola opening upwards with its vertex at (0, 1).

Answer

A parabola opening downwards with its vertex at (1, 0).

Question 30

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

Accepted Answer

b^2 - 4ac

Answer

4ac - b^2

Answer

a^2 - 4bc

Answer

4a^2 - bc

Question 31

Determine the range of the quadratic function y = -x^2 + 4x - 3.

Accepted Answer

(-∞, 1]

Answer

(1, ∞)

Answer

[0, 1]

Answer

[-∞, 1)

Question 32

State the quadratic formula for solving the equation ax² + bx + c = 0.

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a

Answer

x = (b ± √(b² + 4ac)) / 2a

Answer

x = (-b - √(b² - 4ac)) / 2a

Answer

x = (b - √(b² - 4ac)) / 2a

Question 33

Find the equation of the axis of symmetry of the parabola y = x² - 4x + 3.

Accepted Answer

x = 2

Answer

x = -2

Answer

y = -2

Answer

y = 2

Question 34

What is the range of the quadratic function y = x² - 2x + 1?

Accepted Answer

[0, ∞)

Answer

[0, 1]

Answer

(-∞, 0]

Answer

(-∞, ∞)

Question 35

Which of the following is the equation of the axis of symmetry of the parabola: y = -x² + 4x - 5?

Accepted Answer

x = 2

Answer

x = -2

Answer

y = 2

Answer

y = -2

Question 36

Which of the following equations represents a quadratic function?

Accepted Answer

x² - 5x + 6 = 0

Answer

√x + 2 = 5

Answer

y = 4x³ - 2x + 1

Answer

2x + 3 = 7

Question 37

The graphical representation of a quadratic function is a:

Accepted Answer

Parabola

Answer

Hyperbola

Answer

Straight line

Answer

Circle

Question 38

For the equation: x² - 8x + k = 0, what value of k will result in equal roots?

Accepted Answer

16

Answer

-16

Answer

8

Answer

-8

Question 39

What is the y-intercept of the graph of the equation: y = 2x² - 4x + 3?

Accepted Answer

(0, 3)

Answer

(2, 0)

Answer

(3, 0)

Question 40

A ball thrown vertically upwards has its height, h meters, after t seconds given by the equation: h = -5t² + 20t + 2. What is the maximum height reached by the ball?

Accepted Answer

22 meters

Answer

2 meters

Answer

20 meters

Answer

5 meters

Question 41

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

Accepted Answer

x = 2

Answer

x = -2

Answer

y = -2

Answer

y = 2

Question 42

Does the quadratic function y = x² - 6x + 8 have a maximum or minimum value?

Accepted Answer

Minimum

Answer

Neither minimum nor maximum

Answer

Both minimum and maximum

Answer

Maximum

Question 43

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

Accepted Answer

1

Answer

25

Answer

29

Answer

5

Question 44

What are the x-intercepts of the quadratic function y = x² - 4x + 3?

Accepted Answer

(1, 0) and (3, 0)

Answer

(-1, 0) and (3, 0)

Answer

(0, -1) and (0, -3)

Answer

(0, 1) and (0, 3)

Question 45

What are the coordinates of the vertex of the quadratic function y = -2x² + 8x - 3?

Accepted Answer

(2, 5)

Answer

(4, 13)

Answer

(0, -3)

Answer

(-2, -5)

Question 46

Solve the quadratic equation (x - 3)² = 16 for x.

Accepted Answer

x = 7 or x = -1

Answer

x = 8 or x = -8

Answer

x = 6 or x = -6

Answer

x = 4 or x = -4

Question 47

Which of the following quadratic functions has roots at x = 2 and x = -5?

Accepted Answer

y = x² - 7x + 10

Answer

y = x² - 2x + 10

Answer

y = 2x² - 7x + 10

Answer

y = x² + 7x - 10

Question 48

Which of the following graphs represents a quadratic function with a maximum value?

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line

Answer

A circle

Question 49

What is the equation of the axis of symmetry for the quadratic function y = 2(x - 1)² + 3?

Accepted Answer

x = 1

Answer

x = 3

Answer

x = 2

Answer

x = -1

Question 50

Solve the quadratic inequality x² - 4x + 4 > 0 for x.

Accepted Answer

x < 2 or x > 2

Answer

x < 4 or x > 0

Answer

x < 0 or x > 4

Answer

0 < x < 4

Question 51

Which of the following transformations will shift the graph of y = x² to the left by 3 units?

Accepted Answer

y = (x + 3)²

Answer

y = (x - 3)²

Answer

y = x² - 3

Answer

y = x² + 3

Question 52

Find the sum of the roots of the quadratic equation 2x² - 5x + 2 = 0.

Accepted Answer

5/2

Answer

-5/2

Answer

-2/5

Answer

2/5