Homework Practice

Printable assignment

Quadratic Quest: Roots, Graphs and Real-Life Problems

Section A: Roots and Factorisation

Question 1mcq

Which of the following is a quadratic equation?

A.3/x + 2 = 0

B.x² + 5x + 6 = 0

C.x + 1 = 4

D.2x + 7 = 0

Question 2mcq

The roots of x² - 5x + 6 = 0 are:

A.2 and 3

B.-2 and -3

C.1 and 6

D.5 and 6

Question 3mcq

For x² + 4x + 4 = 0, the roots are:

A.Not real

B.Positive only

C.Equal and real

D.Real and distinct

Question 4mcq

What is the discriminant of 2x² - 3x + 1 = 0?

A.5

B.17

C.1

D.-1

Question 5mcq

If the discriminant of a quadratic equation is negative, its roots are:

A.Equal and real

B.Not real

C.Real and distinct

D.Always zero

Question 6mcq

Which pair has sum 7 and product 12?

A.3 and 4

B.1 and 12

C.2 and 6

D.-3 and -4

Section B: Graphs and Applications

Question 7mcq

The graph of y = x² opens:

A.Sideways only

B.Downward

C.As a straight line

D.Upward

Question 8mcq

The graph of a quadratic equation is called a:

A.Triangle

B.Straight line

C.Parabola

D.Circle

Question 9mcq

A ball is thrown upward. Its height over time is often modelled by a quadratic because:

A.The speed is always zero

B.The path is always a straight line

C.The ball moves only sideways

D.The path rises and then falls

Question 10mcq

For y = x² - 4, what is y when x = 3?

A.9

B.-5

C.13

D.5

Question 11mcq

If a parabola opens downward, the coefficient of x² is usually:

A.Positive

B.Zero

C.Always one

D.Negative

Question 12mcq

Why are quadratic equations useful in real-life modelling?

A.They are used only for spelling.

B.They cannot represent change.

C.They only count alphabets.

D.They can model curved relationships such as area or projectile motion.