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Coordinate Geometry
O-Level E Math
Linear Graphs
Equation of slanted lines
$$y = mx + c$$
Equation of vertical lines
$$x = a$$
Equation of horizontal lines
$$y = a$$
Quadratic Graphs
Standard form
$$y = ax^2 + bx + c$$
Factorized form
$$y = a(x - \alpha)(x - \beta) \quad \Rightarrow \quad x\text{-intercepts: } \alpha,\; \beta$$
Completed square form
$$y = a(x - h)^2 + k \quad \Rightarrow \quad \text{turning point } (h,\; k)$$
Coordinate Geometry Formulae
$$\text{Distance} = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$
$$\text{Gradient} = \dfrac{y_1 - y_2}{x_1 - x_2}$$
$$\text{Equation of line: } y = mx + c$$
$$\text{Parallel lines} \iff \text{gradients are equal}$$
Find $x$-intercept: sub $y = 0$
Find $y$-intercept: sub $x = 0$
Find intersection: solve simultaneous equations
Formulas for the Singapore O-Level Elementary Mathematics syllabus