1. 1.1 Graph of Equations How to sketch graphs
Find the intercept of a graph
Use Symmetry to make graphs

2. Equations in 2 variables
1 st degree equations are linear equations for example y = 4x – 6
2 nd degree equations are Quadratic equations for example y = x2 + 2

3. Linear equations Have solutions of order pairs (x, y)
x is part of the domain (input)
y is part of the range (output)
When x = 0, you have the y intercept
When y = 0, you have the x intercept

4. Quadratic equation Graph a Parabola which have
A vertex, a focus and a directrix
Also, an Axis of Symmetry
Symmetry is ability to fold the graph on itself across a point or line.

5. There are 3 types of Symmetry
Symmetric with respect to the x Axis
Here (x, y) and (x, -y) are on the same graph
Symmetric with respect to the y Axis
Here (x, y) and (-x, y) are on the same graph
Symmetric with respect to the origin
Here (x, y) and (-x,-y) are on the same graph

6. Symmetric with respect to the x Axis Here (x, y) and (x, -y) are on the same graph

7. Symmetric with respect to the y Axis Here (x, y) and (-x, y) are on the same graph

8. Symmetric with respect to the origin Here (x, y) and (-x,-y) are on the same graph

9. How to test for Symmetry
Replace y with – y, if it does not change the equation it is symmetry “with respect to the x axis”
x = 4y2 and x = 4(-y)2 are both the same

10. How to test for Symmetry
Replace x with – x, if it does not change the equation it is symmetry “with respect to the y axis”
y = 1/3x2 and y = 1/3(- x)2 are the same

11. Symmetry for the origin
Replace y with – y and x with - x, if it does not change the equation it is symmetry “with respect to the origin”
x2 + y2 = 25 and (- x)2 + ( - y)2 = 25 are the same.

12. How about y = | x – 2| is it Symmetric or not?
We could use a table
You could graph the equation to show
Or use an Symmetry Algebra tests of change x and y.

13. The last thing in this Chapter is the equation of a Circle, you see this in Geometry and Algebra 2
(x- h)2 + (g – k)2 = r2
Do you remember what (h, k) where in the graph?
What does the r stand for in the equation?
How would you find the equation of a circle with a center at (2,3) and a point of (5, 7)?

14. Homework
Page 9-11 #1-4, 5 , 8,12, 15, 24, 25, 28, 35, 42 47, 55, 60, 62, 73, 78, 84, 85, 88, 89