IB Maths AA SL 2.6 Quadratic functions Question Bank

Practise IB Maths AA SL 2.6 by analysing quadratic graphs, roots, vertices and applied quadratic models.

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.

[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
A1A1
N2
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
A1A1
N2
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
A1A1
N2
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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SL 2.6—Quadratic functions question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)