Analysis and Approaches for IBDP Maths Ebook 1 | Page 21

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Exercise 5
1. A quadratic function f can be written in the form f ( x) � a( x � p)( x � 2) . The graph of
f has axis of symmetry x � 1 and y -intercept at (0, � 32) .
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(a) Find the value of p .
(b) Find the value of a .
(c) The line y �4mx
� 57 is a tangent to the curve of f . Find the values of m .
[3]
[3]
[8]
2. A quadratic function f can be written in the form f ( x) � a( x � 4)( x � q)
. The graph of
f has axis of symmetry x � 2.5 and passes through (5, � 4) .
(a) Find the value of q .
(b) Find the value of a .
(c) The line y � mx is a tangent to the curve of f . Find the values of m .
[3]
[3]
[8]
3. A quadratic function f can be written in the form f ( x) � ( x � p)( x � 1) . The graph of f
passes through (3,12).
(a) Find the value of p .
(b) Find the x -coordinate of the vertex of f .
(c) The line y �m( x � 1) is a tangent to the curve of f . Find the values of m .
[3]
[3]
[8]
4. A quadratic function f can be written in the form f ( x) � a( x � p)( x � p)
, where p � 0.
The graph of f passes through (0, � 9) and (1, � 5) .
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(a) Show that a � .
2
p
[2]
(b) Hence, find the values of p and a .
[4]
(c) The line y � �4 mx �(9 � m)
is a tangent to the curve of f . Find the values of m .
[8]
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