IB Maths AA SL 2.6 Quadratic Functions Questions

Practise writing quadratic functions in vertex, factorised or expanded form, using roots and turning points to find parameters and selecting meaningful model solutions.

Exam points

Write a quadratic function in vertex, factorised or expanded form as required.
Use the vertex, axis of symmetry and intercepts to determine unknown parameters.
Interpret a quadratic model and select the physically meaningful root or extremum.

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Study SL 2.6—Quadratic functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 7]

Let $f(x)=3 x^{2}-6 x+p$ . The equation f(x)=0 has two equal roots.

(a)

The graph of f has its vertex on the x-axis.

Find the coordinates of the vertex of the graph of f.

[ 4 ]

METHOD 1
valid approach
eg $\quad x=-\frac{b}{2 a}$
correct working A1
eg $\quad-\frac{(-6)}{2(3)}, x=\frac{6}{6}$
correct answers
eg $\quad x=1, y=0 ;(1,0)$
METHOD 2
valid approach
eg f(x)=0, factorisation, completing the square
correct working
eg $\quad x^{2}-2 x+1=0,(3 x-3)(x-1), f(x)=3(x-1)^{2}$
correct answers
eg $\quad x=1, y=0 ;(1,0)$
METHOD 3
valid approach using derivative
eg $\quad f^{\prime}(x)=0,6 x-6$
correct equation A1
eg $\quad 6 x-6=0$
correct answers
eg $\quad x=1, y=0 ;(1,0)$

(b)

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

[ 3 ]

(i)

[ 1 ]

$\quad a=3$

A1 N1

(ii)

[ 1 ]

$\quad h=1$

A1 N1

(iii)

[ 1 ]

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IB Maths AA SL 2.6 Quadratic Functions Questions question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)