(1) A Cartesian coordinate graph: two axes ("axes" plural of "axis"):
- Horizontal axis is called the x-axis.
- Vertical one is the y-axis.
(2) Coordinates are points on a graph => Format: (x, y)
(3) The centre point of the graph is called the origin (0, 0).
It is the zero point of both the x-axis and the y-axis.
Graph of Equation of a Straight Line
A linear (straight line) equation has a standard form:
y = mx + c
Equation of the Line and its Coordinates
Coordinates are points on the line that satisfies/can be substituted into the equation.
Equation of the line is y = 2x + 8
If the line passes through a coordinate (x,y), => can be used for the (x,y) of the equation : y = mx + c
Gradient
Observation:
1. The gradient/"slope" is positive (2) for (0, -2), (5,8) as it is "ascending" from left to right.
Slope Upward => positive gradient(+m)
2. The gradient/"slope" is -2 for (-5,7), (1-5) as it is "descending" from left to right.
Slope downward => -m
3. When calculating the value of m, the (x,y) must be of the same "set order" =>
y1 - y2 or y2 - y1 NOT y1 - y2
x1 - x2 x2 - x1 x2 - x1
Equation Of Vertical And Horizontal Lines
(1) x = numeric value
-> a vertical line graph
Example:
x=5
(2) y = numerical value
-> a horizontal line graph.
Example:
y=5
Level 2
To find intercept of 2 lines
(1) Use simultaneous equation or
(2) the point of interception of the 2 lines on the graph
Graph of Quadratic Functions
(1) Of the form y= ax2 + bx + c ( b and c can be zero, but a ≠ 0)
(2) All have a line of symmetry
(3) U-shaped
(4) Turning Point:
(i) Positive [+ax2] graph - turning point at the bottom (Minimum point)
(ii) Negative [-ax2] graph - turning points at the top (maximum)
Finding Maximum / Minimum Points
Graph of y = kax(a is positive integer)
Graph of power functions y = axn( n = -2, -1, 0 , 1, 2, 3)
