Coordinate Geometry and Quadratic Functions - Desklib

Coordinate geometry and quadratic
functions
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TABLE OF CONTENTS
QUESTION 1..................................................................................................................................3
i) Gradient....................................................................................................................................3
ii) Equation of line.......................................................................................................................3
QUESTION 2..................................................................................................................................3
i) Gradient....................................................................................................................................3
ii) Equation of line.......................................................................................................................3
iii) Line AB..................................................................................................................................4
iv) Point of intersection on x axis................................................................................................4
QUESTION 3..................................................................................................................................4
(a) Solving inequalities................................................................................................................4
(b) Solving equations...................................................................................................................6
QUESTION 4..................................................................................................................................7
Centre and radius of circle...........................................................................................................7
QUESTION 5..................................................................................................................................8
QUESTION 6..................................................................................................................................9
Finding point of intersection........................................................................................................9
QUESTION 7................................................................................................................................10
Quadratic equations...................................................................................................................10
i).................................................................................................................................................10
ii)................................................................................................................................................10
iii)...............................................................................................................................................11
QUESTION 8................................................................................................................................11
Quadratic equations with graph.................................................................................................11
a)................................................................................................................................................11
b)................................................................................................................................................12
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QUESTION 1
i) Gradient
P (0, -5)
Q (-2, 8)
Gradient for given two points (x1,y1) and (x2, y2) can be obtained by formula: (y2- y1) / (x2 –
x1)
Gradient = [8 – (-5) ] / [-2-0] = 13/-2
Gradient = -6.5
ii) Equation of line
P (0, -5)
Q (-2, 8)
Slope of given points = -6.5
Let slope of perpendicular line is m
As both lines are perpendicular their product is -1
-6.5 m = -1
m = 1/6.5 = 0.15
Perpendicular line passes through origin (0,0) so equation of perpendicular line will be:
y= 0.15x
QUESTION 2
A = (1, -4) B = (3, -7)
i) Gradient
Gradient m = [-7 – (-4)] / [3-1]
= -3/2 = -1.5
Gradient = -1.5
ii) Equation of line
Equation of line = (y – y1) = m (x- x1)
= (y +4) = -1.5 (x- 1)
Line AB : y = -1.5 x – 2.5
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iii) Line AB
iv) Point of intersection on x axis
The point at which line crosses the x axis can be determined by putting y= 0 in the equation of
line AB.
y = -1.5 x – 2.5
When we put y = 0
1.5x = -2.5
x = - 1.66
Thus line crosses x axis at -1.66
QUESTION 3
(a) Solving inequalities
i)
15x -4 ≥ 11 (x-2)
Solution
15x -4 ≥ 11x – 22
4x ≥ -18
x ≥ -4.5
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