Graphing Linear & Quadratic Equations

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Graphing Linear Equations

There are two methods of graphing

1. 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.

2. 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.

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)

This is what our graph should look like.

x + 3y = 9

(0,3)

(9,0)

Slope Intercept Method

33

1

xy

3

1

run

rise1. m=

2. y intercept=3

Remember you always need your equations in the form ofy = mx + b. So let’s try:

Graph of our equation

Y-intercept (0,3)

Graphing Quadratic Functions

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

562 xxy

05565y then 5

35464y then 4

45363y then 3

35262y then 2

05161y then 1

55060y then 0

: when So

2

2

2

2

2

2

x

x

x

x

x

x

0 3- 4- 3- 0 5

5 4 3 2 1 0

y

x

Here’s what our graph looks like

(0,5)

(3, - 4)

(1,0)

(5,0)

(2, -3) (4, -3)

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.

khxay 2

22

22

a

bc

a

bxay

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.

43 2 xy

y-intercept = (0,5)x-intercept = (1,0) and (5,0)

Vertex = (3,-4)

Here are the points on the graph

(0,5)

(3, - 4)

(1,0)

(5,0)

Questions?

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Graphing Links

Graphing Linear and Quadratic Equations Workshop Handout

Graphing Lines Handout Graphing Quadratics Handout Graphing Lines Quiz