2002 by Shawna Haider You should be familiar

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

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

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

Let's put these values in a table: x y 2 0 -1 1 -3 0 -4 -3 -3 5 Now let's plot what we have so far: 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 31(-1) (-3) 3 5 - 3 5 Choose some more x values to plug into the equation to find corresponding y values 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… x y 1 00 -1 0 0 -1 -2 2 -3 1 1 2 Find the x & y intercepts & plot them: 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 0 3 2 could be 1 or -1 Get the y alone Choose some more x values to plug into the equation to find corresponding y values 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".