1. Graphing Linear/Quadratic Equations
April 18th, 2013

2. Warm Up 1) Write in set and interval notation:
“The set of x such that x is greater than or equal to 5 or less than -2”
Complete the tables for the equations & sketch the graphs:
2) f(x) = 3x ) f(x) = x2 - 5x + 6 X Y -1 1 2 3 X Y 1 2 3 4

3. Linear Equations
To graph a linear equation put in slope intercept form: y = mx + b or f(x) = mx + b
“m” represents the slope = rise/run
“b” represents the y-intercept
You can graph a linear equation by starting with the y-intercept. From this point use your slope to find the next point.
If your slope is positive: go up, then to the right
If you slope is negative: go down, then to the right

4. Examples
Graph y = 5x - 3
Graph f(x) = -1/2x + 4

5. You Try!
Graph f(x) = 2/3x - 2
Graph y = -x + 3

6. Review: Find the domain/range of the following graphs!
Domain: Domain: Domain:
Range: Range: Range:
Most of the time for linear graphs the domain/range will be all real numbers, but you should look at your graph to see if there are any restrictions!

7. Quadratic Equations Standard Form: f(x) = ax2 + bx +c
Quadratic equations come in two forms:
Standard Form: f(x) = ax2 + bx +c
Vertex Form: f(x) = a (x - h)2 + k

8. Quadratic Equations In standard form “C” is the y-intercept. (0, C)
The x value of the vertex and the axis of symmetry can be found using
x = –b 2a
After you find the x-value of the vertex, plug in the equation to find the y-value.
You can find the x-intercepts on the calculator, by factoring, or using the quadratic formula!

9. Examples Find the y-int/x-int(s), AOS, and vertex…GRAPH!
f(x) = -x2 - 7x + 8
Domain:
Range:

10. Examples Find the y-int/x-int(s), AOS, and vertex…GRAPH!
F(x) = 4x2 – 6x + 1
Domain:
Range:

11. You Try! Find the y-int/x-int(s), AOS, and vertex…GRAPH!
f(x) = x2 – x + 6
Domain:
Range:

12. Vertex Form: Horizontal Shift
When a quadratic is in vertex form we can see the transformations!
A horizontal shift occurs when adding (left) /subtracting(right) INSIDE of the parentheses:
Parent Shifted
f(x) = (x – 4)2

13. Vertex Form: Vertical Shift
We can have both a horizontal and vertical shift!
A vertical shift occurs when adding (up) /subtracting (down) OUTSIDE of the parentheses:
f(x) = (x - 4)2 + 5
Parent f(x) = x Shifted

14. Examples List the transformations f(x) = (x + 7)2 - 8

15. Examples
Graph the original function and the transformed graph, then list the transformations…
f(x) = x2 f(x) = (x + 3)2 - 2

16. You Try! List the transformations f(x) = (x + 3)2 + 4

17. You Try
Graph the original function and the transformed graph, then list the transformations…
f(x) = x2 f(x) = (x + 5)2 - 4

18. Matching/Worksheet
With the person next to you match the equation with the correct graph and the correct domain and range! You can use more than once.
For the quadratic equations find all of the information and graph! Don’t forget Domain/Range

19. Homework
Worksheet