IB Mathematics SL & HL
quadratic functions & equations – 1 (v2)
answers on next page
4 questions ̶ progressing from ‘accessible’ to ‘discriminating’
1.
The diagram below shows part of the graph of the equation
y = 2 x 2 + ax + b . The graph intersects the x-axis at the points
 7 
 − , 0  and ( 2, 0 ) . Find the value of a and the value of b.
 2 
[ no calculator ]
2.
Consider the function f ( x ) = x 2 − 8 x + 18 .
[ no calculator ]
(a) Show that f ( x )  0 for all real values of x.
(b) Express f ( x ) in the form f ( x ) = ( x + p ) + q .
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(c) The graph of f ( x ) is a parabola. Write down the equation of
the parabola’s axis of symmetry and the coordinates of its vertex.
3.
Find the range of values of k such that the equation 2 x 2 + ( 3 − k ) x + k + 3 = 0
has two distinct real solutions.
4.
[ calculator allowed ]
If  and  are the roots of the quadratic equation x 2 − 3x − 5 = 0 , then find
the quadratic equation that has roots of
(a)  2 and  2
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(b)
[ calculator allowed ]
1
1
and
 +1
 +1
1
IB Mathematics SL & HL
quadratic functions & equations – 1 (v2)
Answers
1.
a = 3, b = −14
2.
(b) f ( x ) = ( x − 4 ) + 2
2
(c) x = 4;
( 4, 2 )
3.
k  −1 or k  15
4.
(a) x 2 − 19 x + 25 = 0
(b) x 2 + 5 x − 1 = 0
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