Functions and Graphs
Linear Equations: Intercept Form
The intercept form is used to write the equation of a line when you
know where it crosses the x-axis and y-axis.
Formula
:
: The x-intercept (where the line crosses the x-
axis at point ).
: The y-intercept (where the line crosses the y-
axis at point ).
Derivation
: This form is derived from the slope-intercept
formula ( ) by substituting the intercepts and
simplifying the expression.
Quadratic Functions & Parabolas
The document covers the properties of quadratic functions, which
take the form .
The Parabola
: The graph of a quadratic function.
If , the parabola opens
upward
(creating a minimum
point).
If , the parabola opens
downward
(creating a
maximum point).
Vertex
: The highest or lowest point of the parabola.
Axis of Symmetry
: The vertical line that passes through the vertex,
dividing the parabola into two matching halves.
Solving Quadratic Inequalities
To solve inequalities like , follow these four steps:
Factorise
: Turn the quadratic expression into two
brackets.
Example
: .
Find Critical Values
: Set each bracket to zero to find the
points where the expression equals zero.
Example
: and .
Determine the Solution Set
: Write the solution using
inequality notation based on the original sign (e.g.,
whether the graph is above or below the x-axis).
Example
: .
Graph on a Number Line
: Represent the solution visually
using open or closed circles.
Key Coordinate Geometry Concepts
+
a
x
=
b
y
1
a
(
a
, 0)
b
(0,
b
)
y
=
mx
+
c
y
=
ax
+
2
bx
+
c
a
> 0
a
< 0
x
+
27
x
+ 10 < 0
(
x
+ 5)(
x
+ 2) < 0
x
= −5
x
= −2
−5 <
x
< −2
