1. Graphing Linear & Quadratic Equations
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2. Graphing Linear Equations
There are two methods of graphing
Since you only need two points to graph a line we can use the intercept method if the equation is written in the standard form of ax + by = c.
The slope intercept is another preferred method. All you need from the equation is the slope and the y-intercept. The equation is in the form y = mx + b.

3. Intercept Method x + 3y = 9 Set x = 0 and solve for y.
Set y = 0 and solve for x.
Then plot the points on the graph and draw a straight line through them as illustrated.
3y = 9
y = 3
x = 9
(0,3), (9,0)

4. This is what our graph should look like.
x + 3y = 9
(9,0)
(0,3)

5. Slope Intercept Method
Remember you always need your equations in the form of
y = mx + b. So let’s try: m=
2. y intercept=3

6. Graph of our equation
Y-intercept (0,3)

7. Graphing Quadratic Functions
To have an accurate drawing of the quadratic function we can plot some values for x. Lets try:

8. Here’s what our graph looks like
(0,5)
(5,0)
(1,0)
(2, -3)
(3, - 4)
(4, -3)

9. Vertex Form
In order to do this we must convert y=ax²+bx+c into the form of
You must complete the square and use h & k for your vertex.
Luckily this formula will help us with completing the square.

10. Applying the Vertex Form
So by doing this we find that our equation
is were our h & k is (3,-4). Now find the x & y intercepts.
y-intercept = (0,5)
x-intercept = (1,0) and (5,0)
Vertex = (3,-4)

11. Here are the points on the graph
(0,5)
(5,0)
(1,0)
(3, - 4)

12. Tutorial Services – The Math Center
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Questions?

13. Graphing Links
Graphing Linear and Quadratic Equations Workshop Handout
Graphing Lines Handout
Graphing Quadratics Handout
Graphing Lines Quiz