Unit 2: Functions

Topic 2.6: Quadratic Functions Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.6. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks

2026

Find the axis of symmetry of y = x² − 8x + 3.

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2Write down2 marks

2026

For

f (x) = - (x - 3)^{2} + 8

, write down (a) the coordinates of the vertex and (b) the maximum value.

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3Find2 marks

2026

Find the x-intercepts of

y = (x - 5) (x + 2)

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4Find2 marks

2026

Find the axis of symmetry of

y = x^{2} - 8 x + 3

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5State2 marks

2026

State the range of

f (x) = (x - 4)^{2} - 2

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6State2 marks

2026

State the range of f(x) = (x − 4)² − 2.

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7Write down2 marks

2026

For

y = 3 x^{2} - 12 x + 7

, write down (a) the direction it opens and (b) the y-intercept.

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8Find3 marks

The function f is defined by f(x) = 2x² − 8x + 3, x ∈ ℝ. Find the minimum value of f and hence write down the range of f.

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9Find2 marks

The function g is defined by g(x) = −x² + 6x − 4, x ∈ ℝ. Find the maximum value of g and write down the range of g.

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10Choose1 mark

For

y = - 2 x^{2} + 8 x - 5

, state which way the parabola opens and its y-intercept.

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11Choose1 mark

For

g (x) = - 3 (x - 2)^{2} + 11

, write down the maximum value and where it occurs.

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12Choose1 mark

A parabola has x-intercepts at

x = - 5

and

x = 3

. State its axis of symmetry.

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13Choose1 mark

Write

y = (x + 3) (x - 7)

in the form

y = a x^{2} + b x + c

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14Determine1 mark

2026

It is given that x² − 4x + 13 = (x − 2)² + 9.

Hence, determine the minimum value of √(x² − 4x + 13).

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15Choose1 mark

Where does the curve

y = 2 (x - 1) (x + 6)

cut the x-axis?

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16Show that1 mark

2026

Show that the axis of symmetry is

x = 3

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17Show that1 mark

2026

Show that the maximum value of

f

7

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18Write down2 marks

2026

For f(x) = −(x − 3)² + 8, write down (a) the coordinates of the vertex and (b) the maximum value.

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19Find1 mark

2023

Two numbers add up to

20

. Determine the first number

x

for which their product

x (20 - x)

is as large as possible.

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20Show that1 mark

2023

Show that the least value of

x^{2} - 8 x + 20

4

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