Quadratic Equations Quiz

Question 1

What is the standard form of a quadratic equation?

Accepted Answer

ax² + bx + c = 0

Answer

y = mx + c

Answer

ax + b = 0

Answer

x² = c

Question 2

Solve by factorising: x² + 5x + 6 = 0

Accepted Answer

x = −2 or x = −3

Answer

x = 2 or x = 3

Answer

x = 1 or x = 6

Answer

x = −1 or x = −6

Question 3

Solve: x² − 7x + 12 = 0

Accepted Answer

x = 3 or x = 4

Answer

x = −3 or x = −4

Answer

x = 6 or x = 2

Answer

x = 1 or x = 12

Question 4

What is the quadratic formula?

Accepted Answer

x = (−b ± √(b² − 4ac)) / 2a

Answer

x = (b ± √(b² − 4ac)) / 2a

Answer

x = (−b ± √(b² + 4ac)) / 2a

Answer

x = (b ± √(b² + 4ac)) / a

Question 5

Use the quadratic formula to solve: x² + 4x − 5 = 0

Accepted Answer

x = 1 or x = −5

Answer

x = −1 or x = 5

Answer

x = 2 or x = −5

Answer

x = 5 or x = −1

Question 6

What is the discriminant of ax² + bx + c = 0, and what does it tell you?

Accepted Answer

b² − 4ac; whether the equation has real solutions

Answer

b² + 4ac; whether the equation has integer solutions

Answer

√(b² − 4ac); the number of solutions

Answer

2a; whether the parabola opens up or down

Question 7

How many real solutions does x² + 2x + 5 = 0 have?

Accepted Answer

None

Answer

Two

Answer

One

Answer

It depends on x

Question 8

Solve: x² − 9 = 0

Accepted Answer

x = 3 or x = −3

Answer

x = 9

Answer

x = 3 only

Answer

x = 81

Question 9

Complete the square: write x² + 6x + 2 in the form (x + a)² + b.

Accepted Answer

(x + 3)² − 7

Answer

(x + 6)² − 34

Answer

(x + 3)² + 2

Answer

(x + 3)² − 11

Question 10

Solve: 2x² − 8 = 0

Accepted Answer

x = ±2

Answer

x = 2

Answer

x = ±4

Answer

x = 4

Question 11

Factorise: x² − 25

Accepted Answer

(x + 5)(x − 5)

Answer

(x − 5)²

Answer

(x − 5)(x − 5)

Answer

(x + 25)(x − 1)

Question 12

Solve: x² + x − 6 = 0

Accepted Answer

x = 2 or x = −3

Answer

x = −2 or x = 3

Answer

x = 6 or x = −1

Answer

x = 3 or x = 2

Question 13

A ball is thrown upward. Its height h = −5t² + 20t. When does it hit the ground (h = 0)?

Accepted Answer

t = 0 or t = 4 seconds

Answer

t = 2 seconds

Answer

t = 4 seconds

Answer

t = 5 seconds

Question 14

The parabola y = x² − 4x + 3. What are its x-intercepts?

Accepted Answer

x = 1 and x = 3

Answer

x = −1 and x = −3

Answer

x = 2 and x = 1

Answer

x = 4 and x = 0

Question 15

Solve: 3x² − 12x = 0

Accepted Answer

x = 0 or x = 4

Answer

x = 4 only

Answer

x = 0 only

Answer

x = 0 or x = 12

Question 16

What is the vertex (turning point) of y = (x − 3)² + 5?

Accepted Answer

(3, 5)

Answer

(−3, 5)

Answer

(3, −5)

Answer

(5, 3)

Question 17

Solve using the quadratic formula: 2x² + 3x − 2 = 0

Accepted Answer

x = 0.5 or x = −2

Answer

x = 1 or x = −2

Answer

x = 2 or x = 0.5

Answer

x = −0.5 or x = 2

Question 18

Which of these quadratics has exactly one repeated root?

Accepted Answer

x² − 6x + 9

Answer

x² + 4x + 3

Answer

x² + 2x + 5

Answer

x² − x − 2

Question 19

The sum of a number and its square is 20. Which equation models this?

Accepted Answer

x² + x − 20 = 0

Answer

x + x² = 20

Answer

x² − x − 20 = 0

Answer

2x² = 20

Question 20

Which direction does the parabola y = −3x² + 2x − 1 open?

Accepted Answer

Downward, because a < 0

Answer

Upward, because a > 0

Answer

Left, because b < 0 is absent

Answer

Right, because c < 0