Quadratic Equations: Master the Art of Solving Quadratics

Question 1

Factorise the quadratic expression: x² + 5x + 6

Accepted Answer

(x + 2)(x + 3)

Answer

(x + 3)(x + 2)

Answer

(x - 2)(x - 3)

Answer

(x - 3)(x - 2)

Question 2

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

Accepted Answer

(2, 3)

Answer

(0, 3)

Answer

(2, -5)

Answer

(-2, -5)

Question 3

Factorize the quadratic expression x² - 4x + 4:

Accepted Answer

(x - 2)²

Answer

(x + 2)²

Answer

x(x - 4)

Answer

Cannot be factorized

Question 4

Solve the equation (x + 2)² = 9:

Accepted Answer

x = -1 or x = 5

Answer

x = 1 or x = -5

Answer

x = 2 or x = -7

Answer

x = -2 or x = 7

Question 5

Factor the quadratic expression (x^2 - 10x + 25).

Accepted Answer

(x - 5)^2

Answer

(x + 5)^2

Answer

(x - 5)(x + 5)

Answer

(x + 25)(x - 1)

Question 6

Find the discriminant of the quadratic equation (ax^2 + bx + c = 0).

Accepted Answer

b^2 - 4ac

Answer

b^2 + 4ac

Answer

a^2 - 4bc

Answer

a^2 + 4bc

Question 7

Which of the following is the graph of the quadratic equation (y = -x^2 + 6x - 8)?

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line with a positive gradient

Answer

A straight line with a negative gradient

Question 8

Which of the following is a quadratic inequality?

Accepted Answer

x^2 + 4x - 5 < 0

Answer

x^2 > 9

Answer

x^3 - 2x^2 + 1 ≥ 0

Answer

x^4 + x^2 - 2 > 0

Question 9

Factorise the quadratic expression x² - 9:

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)²

Answer

(x + 3)²

Question 10

Find the discriminant of the quadratic equation 2x² + 5x - 3 = 0:

Accepted Answer

25

Answer

1

Answer

5

Answer

33

Question 11

Which of the following is the equation of the axis of symmetry of the parabola y = 2x² - 4x + 1?

Accepted Answer

x = 1

Answer

x = -1

Answer

y = 1

Answer

y = -1

Question 12

Solve 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 13

Which of the following graphs represents a quadratic equation with a positive leading coefficient?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A straight line

Answer

A circle

Question 14

Determine the vertex of the parabola represented by the quadratic equation: y = -x² + 4x + 2

Accepted Answer

(2, 6)

Answer

(-2, -2)

Answer

(2, -2)

Answer

(-2, 6)

Question 15

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

Accepted Answer

b² - 4ac

Answer

4ac - b²

Answer

b²/4 - a

Answer

a² + b²

Question 16

Calculate the discriminant of the quadratic equation 2x² + 3x - 5 = 0.

Accepted Answer

13

Answer

1

Answer

9

Answer

25

Question 17

Which value of the discriminant indicates that a quadratic equation has only one real root (repeated root)?

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Question 18

What are the key features of a parabola defined by a quadratic equation?

Accepted Answer

Vertex, axis of symmetry, domain, and range

Answer

Intercepts, turning points, and range

Answer

Roots, vertex, and y-intercept

Question 19

Determine the minimum value of the quadratic function: f(x) = x² + 4x + 5

Accepted Answer

-1

Answer

2

Answer

1

Answer

0

Question 20

Solve the quadratic equation by factorization: **x² - 5x + 6 = 0**

Accepted Answer

**x = 2 or x = 3**

Answer

x = -2 or x = -3

Answer

x = 4 or x = 5

Answer

x = 1 or x = 6

Question 21

Which of the following is the equation of the axis of symmetry of the parabola **y = x² - 4x + 3**?

Accepted Answer

**x = 2**

Answer

x = 1

Answer

x = 3

Answer

x = -2

Question 22

Find the range of the quadratic function **y = -x² + 4x + 3**

Accepted Answer

**[-1, ∞)**

Answer

(-∞, -1]

Answer

(-∞, 3]

Answer

(3, ∞)

Question 23

Which of the following is the quadratic formula?

Accepted Answer

**x = (-b ± √(b² - 4ac)) / 2a**

Answer

V = πr³

Answer

A = lw

Answer

x² + y² = r²

Question 24

Find the vertex of the parabola **y = -x² + 4x - 3**.

Accepted Answer

**(2, 1)**

Answer

(2, -1)

Answer

(1, 2)

Answer

(-2, 1)

Question 25

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

Accepted Answer

**ax² + bx + c = 0**

Answer

V = πr²h

Answer

r = a(1 - cosθ)

Answer

y = mx + b