IB Mathematics Analysis and Approaches Topic SL 2.6—quadratic Function Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.6—quadratic Function Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.6—quadratic Function with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.6—quadratic Function and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

SLPaper 2

A quadratic model $f (x) = a x^{2} + b x + c$ is fitted to three measured points $P (1, ln 5)$ , $Q (4, 1.5 + ln 10)$ , $R (7, 1 + ln 4)$ .

Determine $a, b, c$ (numerically). Give your values correct to 3 significant figures.

[5]

Write $f (x)$ in vertex form $f (x) = a (x - h)^{2} + k$ . Hence state the vertex and the range of $f$ for $x \in R$ . Give $h, k$ to 3 d.p.

[4]

Let $g (x) = ln (x + 2) + 1$ . Solve $f (x) = g (x)$ for $x \geq 0$ , giving $x$ correct to 3 d.p., and justify the number of solutions.

[6]

Solve $f (x) \geq g (x)$ for $x \geq 0$ .

[3]

Question 2

SLPaper 1

The quadratic function is defined as $f (x) = a x^{2} + b x + c$ , where $a, b, c \in R$ . The graph of $f$ intersects the line $y = 2 x + 4$ at exactly one point, and the vertex of the parabola is at $(- 1, 3)$ .

Show that $a = 1$ .

[6]

Find the values of $b$ and $c$ .

[2]

Question 3

SLPaper 1

The quadratic function is defined as $f (x) = p x^{2} + q x + r$ , where $p, q, r \in R$ . The graph of $f$ has a vertex at $(3, - 2)$ and is tangent to the line $y = - x + 7$ .

Show that $p = - \frac{1}{24}$ .

[6]

Find the values of $q$ and $r$ .

[2]

Express $f (x)$ in the form $f (x) = p (x - s) (x - t)$ , and state the values of $s$ and $t$ .

[2]

Question 4

SLPaper 1

Let $f (x) = 3 x^{2} - 12 x + 9$ , for $x \in R$ .

Write down the value of $f (0)$ .

[1]

Solve the equation $f (x) = 0$ .

[3]

The function $f$ can be written in the form $f (x) = a (x - h)^{2} + k$ .

Find the values of $a$ , $h$ and $k$ .

[3]

For the graph of $f$ , write down:

the coordinates of the vertex;

the equation of the axis of symmetry.

[2]

The graph of a function $g$ is obtained from the graph of $f$ by a reflection in the $x$ -axis, followed by a translation by the vector $(- 2 1)$ .

Find $g (x)$ , giving your answer in the form $g (x) = p x^{2} + q x + r$ .

[4]

Question 5

SLPaper 2

A quadratic model $f (x) = a x^{2} + b x + c$ is fitted to three measured points $P (1, ln 3)$ , $Q (3, e)$ , $R (6, 2 + ln 7)$ .

Determine $a$ , $b$ and $c$ , giving each value to 3 significant figures.

[5]

Write $f (x)$ in vertex form $f (x) = a (x - h)^{2} + k$ . Hence state the vertex and the range of $f$ . Give $h, k$ to 3 d.p.

[4]

Let $g (x) = ln (x + 2) + 1$ . Solve $f (x) = g (x)$ for $x \geq 0$ to 3 d.p. Justify the number of solutions on $x \geq 0$ .

[6]

IB Mathematics Analysis and Approaches SL 2.6—quadratic Function Questionbank

IB Mathematics Analysis and Approaches SL 2.6—quadratic Function Questionbank

Unlock all 13 questions with a free account

IB Mathematics Analysis and Approaches SL 2.6—quadratic Function Questionbank

IB Mathematics Analysis and Approaches SL 2.6—quadratic Function Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.6—quadratic Function Questionbank

Unlock all 13 questions with a free account