Draw Graph Of An Equation
Equation type is set to quadratic
but you can change it
Select Linear for straight line graph

DOWNLOAD FREE GRAPH PAPER
Graphing Ellipses And Hyperbolas

GRAPHS

The x,y rectangular coordinate system is shown in the first videos
and the drawing of graphs is shown on the videos further down the page

 

Video
The x,y Rectangular Coordinate System

The Horizontal Axis - The x Axis
The Vertical Axis - The y Axis
The Origin - Where The Horizontal Axis Crosses The Vertical Axis
Quadrant 1 - The First Quadrant - The Top Right Quadrant
Quadrant 2 - The Second Quadrant - The Top Left Quadrant
Quadrant 3 - The Third Quadrant - The Bottom Left Quadrant
Quadrant 4 - The Fourth Quadrant - The Bottom Right Quadrant

 

Video
The x,y Rectangular Coordinate System

This video includes showing how to plot more difficult points
such as those involving a zero
and those where there may be fractions, decimals or mixed numbers

 

The three main methods of graphing
the equation of a straight line

But you may use a combination of methods
if appropriate in the circumstances of a particular question

The next two videos cover these three methods
and then the methods are summarised in writing

Equations of Lines (Part 1)

Equations of Lines (Part 2)

[1] Table Of Values Method

Ordered pairs of x and y are found.
This is often done by substituting an x value into the equation
and finding a corresponding y value
Such ordered pairs are often set out in a table
If a minimum of three ordered pairs are found and plotted
it will be easy to see if one of them is incorrect
because that particular point will be out of line with the others
This method works for all linear (straight line) equations
and will also work for other types of equations such as quadratic

[2] Intercept - Intercept Method

Ordered Pairs where one of the pair is zero
giving (0, ...) which will be the point on the y-axis
where the line intercepts the y-axis, and
giving (... ,0) which will be the point on the x-axis
where the line intercepts the x-axis
This is a quick way of graphing the equation
BUT because only two points are used there is no room for error
Once the line is drawn another point on the line can be checked
to see if the x and y values of the point work in the equation

[3] Slope - Intercept

Plot the intercept point on the y-axis
Use the slope of the line to plot other points
This method usually depends on having or putting
the equation in Slope - Intercept Form ( y = mx + c )
and requires understanding of the how slope and intercept work

 

Video
Using Ordered Pairs Of x And y (Paired Data)
To Draw A Straight Line Graph

 

Video
Using x And y Intercepts
To Draw A Straight Line Graph

 

Video
Using A Table
Of Ordered Pairs Of x And y (Paired Data)
To Draw A Straight Line Graph
Part 1 of 2

 

Video
Using A Table
Of Ordered Pairs Of x And y (Paired Data)
To Draw A Straight Line Graph
Part 2 of 2

 

Video
Graphing Linear Equation
Drawing Straight Line Equation
Using
[1] The y Intercept
[2] The Slope (Gradient) Of The Line

The case where the equation is already in Slope - Intercept Form

 

Video
Graphing Linear Equation
Drawing Straight Line Equation
Using
[1] The y Intercept
[2] The Slope (Gradient) Of The Line

The case where we have to change the equation into Slope - Intercept Form

 

Video
Graphing A Quadratic Curve
Graphing A Quadratic Function
Drawing An 'x squared' Graph
Using A Table Of Values
y = x2 + 4x + 3

 

Video
Graphing The Quadratic Function
y = x2 + 4x + 3
Finding The Domain
Finding The Range
Compare With Graph Of The Function y = x2

 

Vertical And Horizontal Transformations Of Graphs

 

Transformations Of The Sine Graph

 

Exponential Graph

 

Logarithmic Graph

 

Rates of Change and the Slope of a Curve


 

Lecture On Graphs

Question / Comment / Suggestion

Horizontal
Straight Line Graph
y = c

Vertical
Straight Line Graph
x = a

Linear Graphs
Straight Line Graphs
The links below are to pages with interactive graphs of the type shown

y = x

y = 2x

y = x + 1

y = 2x + 1

y = gradient × x
y = mx
y = ax

y = x + intercept
y = x + c
y = x + b

y = gradient × x + intercept
y = mx + c
y = mx + b
y = ax + b


LINKS
Interactives

Absolute Value Functions
y = a |x - b| + c

Quadratic Functions
[Parabolas]
y = ax2 + bx + c

Quadratic Functions
[Parabolas]
y = a(x - h)2 + k

Cubic Functions
y = ax3+bx2+cx+d

Square Root Functions
y = a (x-b)1/2 + c

Power Function
y = xb, x > 0

mathdemos.gcsu.edu


LINK
Online 3-D Graph Plotter WolframResearch
Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.