Graphing Linear & Quadratic Equations Brought to you by Tutorial Services – The Math Center

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.

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 (9,0) (0,3)

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

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:

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

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)

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

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