1. Chapter 8: Graphs and Functions

2. Rectangular Coordinate System
8.1

3. Rectangular Coordinate System
8.1
Rectangular Coordinate System

4. Distance and Midpoint Formulas
8.1

5. Circles
8.1

6. Lines and Slopes
8.2
Equations of the form Ax + By = C can be visualized as a straight line
Slope is rise/run
x-intercept: set y = 0
y-intercept: set x = 0

7. Equations of Straight Lines
8.2 & 8.3
Given the slope m and the y-intercept b, the slope-intercept form is
y = mx + b
Given a point (x1,y1) and the slope m, the point-slope form is
y-y1 = m(x-x1)

8. Parallel and Perpendicular
8.2
Parallel lines have the same slope
Ex: y = 2x + 1 and y = 2x – 4
Perpendicular lines have slopes that are negative reciprocals
Ex: y = 2x + 1 and y = -(1/2)x +3

9. Functions A relation is a set of ordered pairs
8.4
A relation is a set of ordered pairs
A function is a relation in which for each value of the first component of the ordered pairs there is exactly one value of the second component
Graph of a function obeys the vertical line test: any vertical line crosses at most once

10. Domain and Range
8.4
When ordered pairs are of the form (x,y), x is the independent variable and y is the dependent variable
The domain is the set of all values of the independent variable x
The range is the set of all values of the dependent variable y

11. Linear Functions A function that can be written in the form
8.4
A function that can be written in the form
f(x) = mx + b
for real numbers m and b is a linear function.
Example: cost and revenue models

12. Quadratic functions A function f is a quadratic function if
8.5
A function f is a quadratic function if
f(x) = ax2 + bx + c
where a, b, and c are real numbers with a not equal to 0.

13. Graphing Quadratic Functions
8.5
The graph of the quadratic function defined by f(x) = a(x-h)2 + k, a not 0, is a parabola with vertex (h,k) and the vertical line x = h as axis of symmetry
The graph opens up if a is positive and down if a is negative
The graph is wide if |a|<1 and narrow if |a|>1 compared to y = x2

14. More Graphing Quadratics
8.5
f(x) = ax2 + bx + c
Decide if graph opens up or down
Find y-intercept by setting x = 0
Find x-intercept by solving f(x) = 0
Find vertex: x = -b/(2a)
Complete the graph

15. 8.5 #41
Steve has 100 meters of fencing material to enclose a rectangular exercise run for his dog. What width will give the enclosure the maximum area?

16. 8.5 #47