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.

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Paper

Level

Difficulty

Question 1SLPaper 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) . \dots

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Question

SLPaper 1Standard

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

(a)

(a) Show that $a=1$ .

[6]

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(b)

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

[2]

SLPaper 1Standard

(a)

[6]

(b)

[2]

(c)

[3]

SLPaper 1Standard

(a)

[1]

(b)

[3]

(c)

[3]

(d)

[2]

SL & HLPaper 1Demanding

(a)

[6]

(b)

[4]

(c)

[3]

(e)

(e) 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 $\binom{1}{-2}$ .

[4]

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b

,

c

∈

R

f

y=2 x+4

(-1,3)

2

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Question 3

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Question 4

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Question 5

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

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

(b) Find the values of $q$ and $r$ .

(c) Find the coordinates of the point where the graph of $f$ touches the line $y=-x+7$ .

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

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

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

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

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

(d) For the graph of $f$ , write down:

the coordinates of the vertex;

the equation of the axis of symmetry.

Let $f(x)=a(x-h)^2+k$ and $g(x)=a(x-m)^2+n$ , where $a \neq 0$ .

The function $s$ is defined by $s(x)=f(x)+g(x)$ .

(a) Show that the vertex of the graph of $s$ is $\left(\frac{h+m}{2},\ k+n+\frac{a(m-h)^2}{2}\right)$ .

(b) Given that $f(x)=3(x-2)^2-5$ and $g(x)=3(x+4)^2+1$ , write $s(x)$ in the form $A(x-H)^2+K$ .

(c) The function $g$ is now replaced by $g(x)=3(x+4)^2+n$ , with $f$ unchanged. Find the value of $n$ for which the graph of $s$ touches the $x$ -axis.

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)

Find $g(x)$ , giving your answer in the form $g(x) = px^2 + qx + r$ .

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

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