Graphs of Equations © 2002 by Shawna Haider

Quadrant II where x is negative and y is positive You should be familiar with the rectangular coordinate system and point plotting from an earlier algebra course. Let's just run through the basics. y axis Quadrant II where x is negative and y is positive Quadrant I where both x and y are positive x axis origin Quadrant IV where x is positive and y is negative Quadrant III where both x and y are negative

Let's plot the point (-3,-5) 8 7 6 5 4 3 2 1 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 -2 -3 -4 -5 -6 -7 Let's plot the point (0,7) Let's plot the point (-3,-5)

This means then that y = -4 and the y intercept is (0,-4) In this section we are going to use the point plotting method to graph equations. Look at the following equation. y = x2 - 4 Recall how to find x and y intercepts. The x intercept is where the y value is zero. The y intercept is where the x value is zero. 0 = x2 - 4 Solving for x y = 02 - 4 Since x2 is 4, x could be 2 or –2 so the x intercepts are (2,0) and (-2,0) This means then that y = -4 and the y intercept is (0,-4)

Let's put these values in a table: 1 3 (-3) (-1) - 3 5 5 x 2 - 2 0 -1 1 -3 3 y 0 0 - 4 - 3 - 3 5 5 Choose some more x values to plug into the equation to find corresponding y values Now let's plot what we have so far: 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 Now let's plot these values and join the points in a smooth curve The shape of this graph is called a parabola. We'll learn more about them later in the course.

Helps to Graph an Equation Isolate (get alone) one of the variables if possible (usually y) Find the x and y intercepts by plugging 0 in for y and then for x like we did on the previous screen (sometimes easier to do this before you isolate a variable) Make a table of values choosing some x values and find corresponding y values (if you isolated x then choose some y values and find corresponding x values) Plot these points and join in a smooth curve or line

Let's try graphing one more… could be 1 or -1 Let's try graphing one more… Get the y alone x 1 -1 -2 2 -3 3 y 0 0 -1 1 1 2 2 Choose some more x values to plug into the equation to find corresponding y values Find the x & y intercepts & plot them: 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 Now let's plot these values and join the points in a smooth curve (or line) The shape of an absolute value graph is "v-shaped".