2. Let's just run through the basics. x axis y axis origin Quadrant I where both x and y are positive Quadrant II where x is negative and y is positive Quadrant III where both x and y are negative Quadrant IV where x is positive and y is negative

3. 2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 Let's plot the point (6,4) Let's plot the point (-3,-5) Let's plot the point (0,7) Let's plot the point (-6,0)

4. In this section we are going to use the point plotting method to graph equations. Look at the following equation. Now lets determine the x and y intercepts. The x intercept is where the y value is zero. 0 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. 0 This means then that y = -4 and the y intercept is (0,-4) +4 Solving for x

5. 2-7-6-5-4-3-21573 0468 2 3 5 6 8 -2 -4 -6 -7 7 1 4 -3 -5 Let's put these values in a table: Now let's plot what we have so far: Choose some more x values to plug into the equation to find corresponding y values (-1) - 3 0 0 - 4 x y 2 - 2 0 5 5 1 (-3) 3 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. - 3 5 -1 1 -3 3 5

6. 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

7. 2-7-6-5-4-3-21573 0468 2 3 5 6 8 -2 -4 -6 -7 7 1 4 -3 -5 Find the x & y intercepts & plot them: Choose some more x values to plug into the equation to find corresponding y values 1 0 x y 0 2 2 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". 1 -2 2 -3 3 Let's try graphing one more… Get the y alone 0 could be 1 or -1 0 1 -1 0

8. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au