1. Warm-up: Graph the equation y = |x – 1|
HW: pg (2, 6, 9, 11, 14, 16, 22, 24, 30, 32, matching, symmetry only: even 40-52)

2. Objectives: To graph equations. To find the intercepts of a graph.
To use symmetry as an aid to graphing.

3. Vocabulary: Graph of an Equation
A visual representation of the set of all points that are solutions of the equation
Solution Point
An ordered pair (a, b) is a solution point of an equation in x and y if the equation is true when a is substituted for x and b is substituted for y.
Intercepts
Points at which the graph intersects the x- or y-axis.

4. Graph of an Equation
The graph of an equation gives a visual representation of all solution points of the equation.

5. How to graph? Point-plotting method construct a table of values.
pros easy
cons if the graph shape is unknown the critical points could be missed
y = |x + 1| x y -3 2 -2 1 -1

6. Know Equation “Types” Linear:
Slope-intercept form y = mx + b, m slope, b y-int
Quadratic:
Parabolas y = ax2 + bx + c, x-coord of vertex –b/2a or
y = a(x – h)2 + k, vertex (h, k)
Absolute Value:
 y = a|x – h| + k, vertex (h, k)

7. Intercepts
The x-intercept of a graph is where it intersects the x-axis.
(a, 0)
The y-intercept of a graph is where it intersects the y-axis.
(0, b)

8. Exercise 1
How many x- and y-intercepts can the graph of an equation have?
No x-intercepts
One y-intercept
Three x-intercepts
One y-intercept
One x-intercept
Two y-intercepts
No intercepts

9. Exercise 2
Given an equation, how do you find the intercepts of its graph?
To find the x-intercepts,
set y = 0 and solve for x.
To find the y-intercepts,
set x = 0 and solve for y.

10. Exercise 3 Find the x- and y-intercepts of y = – x2 – 5x. y-int = 0
to find y-int let x = 0
to find x-int let y = 0
y-int = 0
(0, 0)
x-ints = 0, -5
(0, 0), (-5, 0)

11. Symmetry
A figure has symmetry if it can be mapped onto itself by reflection or rotation.
Click me!

12. Exercise 4
How would an understanding of symmetry help you graph an equation?

13. Symmetry When it comes to graphs, there are three basic symmetries:
x-axis symmetry: If (x, y) is on the graph, then (x, -y) is also on the graph.

14. Symmetry Check the equation for x-axis symmetry: y2 = x + 4
Replace y with -y
x-axis symmetry

15. Symmetry When it comes to graphs, there are three basic symmetries:
y-axis symmetry: If (x, y) is on the graph, then (-x, y) is also on the graph.

16. Symmetry Check the equation for y-axis symmetry: y = x2 – 2
Replace x with -x
y-axis symmetry

17. Symmetry When it comes to graphs, there are three basic symmetries:
Origin symmetry: If (x, y) is on the graph, then (-x, -y) is also on the graph.
(Rotation of 180)

18. Symmetry Check the equation for origin symmetry: y = x3 – 4x
Replace x with -x Replace y with -y
origin symmetry

19. Exercise 5
Using the partial graph pictured, complete the graph so that it has the following symmetries:
x-axis symmetry
y-axis symmetry
origin symmetry

20. Summary: To graph equations. To find the intercepts of a graph.
To use symmetry as an aid to graphing.

21. Sneedlegrit:
Check the equation for x-axis, y-axis, and origin symmetry. y = -2x2 + 3
HW: pg (2, 6, 9, 11, 14, 16, 22, 24, 30, 32, matching, symmetry only: even 40-52)