Download BP03 Straight Line and Functions

Straight Line & Functions
1.
Find the equation of the line through the point (2 , -3) which is parallel to
the line with equation 5x + 3y – 2 = 0.
2.
Find the equation of the median AD of triangle ABC where the coordinates of
A, B and C are (-2 , 3), (-3, -4) and (5 , 2) respectively.
3.
Find the equation of the perpendicular bisector of the line joining A(2 , -1) and
B(8 , 3).
4.
A triangle ABC has vertices A(-4 , -3), B(-2 , 1) and C(6 , -3)
B(-2 , 1)
y
0
x
C(6 , -3)
A(-4 , -3)
(a) Show that the triangle ABC is right-angled at B.
(b) The medians AD and BE intersect at M.
(i) Find the equations of AD and BE.
(ii) Find the coordinates of M.
5.
(a) Express x2 – 8x + 3 in the form (x – a)2 – b and write down the values
of a and b.
(b) Make a sketch of the graph of y = x2 – 8x + 3 indicating where the curve
cuts the y-axis and the turning point.
6.
(a) Express 7 – 2x – x2 in the form a – (x + b)2 and write down the values
of a and b.
1
(b) State the minimum value of
and justify your answer.
7  2x  x 2
7.
f(x) = 2x. Make separate sketches of the following graphs:
(a) y = f(x)
(b) y = 2x + 3
(c) y = 2(x – 4)
8.
x2 1
and h(x)  g ( f ( x))
x2 1
(a) Find a formula for h(x)
(b) For what values of x is h undefined?
f ( x)  2 x  1 , g ( x) 