# Mathematics Methods Formula Notes

All the formulas for Maths Methods 1+2 (Australia). I got it from the website www.vcehelp.com.au and it's really helpful!

- Created by: Meg
- Created on: 26-01-11 00:10

First 505 words of the document:

Downloaded from www.vcehelp.com.au

Created by VCE student Nicholas Buttigieg for Maths Methods Unit 1/2

Here is an article for all of the functions and graphs used in Maths Methods Units 1 & 2. You

can use these as study notes if you like. To look for any diagrams on the shape of graphs,

refer to your textbook.

Linear Graphs

· The form is y = mx + c, where m is the gradient and c is the y-intercept.

· The gradient between two points is equal to m = =

· Two lines with the same gradient are parallel to each other and do not intersect.

· To find the equation of a straight line given two points, use the formula:

m(x - x1) = y - y1, where m is the gradient.

· When given equations of the form ax + by + c = 0, then transpose to y = mx + c

· Vertical lines are of the form x = a, where the x-axis intercept is given as (a, 0).

· Horizontal lines are of the form y = c, where the y-axis intercept is given as (0, c).

· Perpendicular lines can be calculated using the formula: m1 m2 = -1.

· To calculate the tangent of the angle of slope, calculate the gradient, then substitute

it into tan to get the angle.

· The distance between two points is given as

· The midpoint of a line segment is given as

Parabolas

· The form is y = ax2 + bx + c, which is known as polynomial form.

· The form is y = a (x b)2 + c, which is known as turning point form.

· Parabolas of the form y = ax2, in which the axis of symmetry is x = 0, and the turning

point is (0,0). If a is greater than 1, the graph will be narrower than y = x2. If it is

between 0 and 1, the graph will be wider. If a is negative, then the graph is inverted

or reflected in the x-axis.

· Parabolas of the form y = ax2 + c involve a translation up or down the y-axis. The

axis of symmetry is x = 0 and the turning point is (0, c), which correlates to the y-

intercept.

· Parabolas of the form y = a(x b)2 involve a translation left or right along the x-axis.

The axis of symmetry is x = -b and the turning point is (-b, 0), which correlates to the

x-intercept.

· The turning point of a parabola is (-b, c) from the turning point form.

· The turning point of a parabola from polynomial form can be found by completing the

square so it is in turning point form.

· To find x-intercepts, either factorise the equation or use the quadratic formula:

x=

· The axis of symmetry is x = -b from the turning point form.

· The axis of symmetry is x = from the polynomial form.

· The discriminant is equal to = b2 4ac.

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