1. Chapter 6 Algebra *Linear and Nonlinear Functions
*Graphing Quadratic Functions

2. 12-1: Linear and Nonlinear Functions
*Linear Function * Nonlinear Function
- Straight lines indicating a constant rate of change.
Curved line indicating that there is NOT a constant
rate of change.
Therefore, we can identify linear and nonlinear functions simply by looking at the graph!
**Another method is to examine the equation of the function.
Linear Nonlinear
Slope-intercept form: y = mx +b Cannot be written in slope-intercept form
Ex: y = x Slope tells us there is a constant rate of change! Ex: y = 6/x Since x is in the denominator,
it cannot be written in
m = 1 and b = slope-intercept form.

3. Even a table can help us identify!X Y 20 5 16 10 12 15 8 X Y 2 4 20 6 54 8
104
Is the rate of change
constant or is it
increasing/decreasing
at different rates?
Let's Try...
Determine whether each represents a linear or nonlinear function. 1. 2.
y = 5x2 + 3
4. y – 4 = 5x
y = -x + 3
y = 2 –x/2 + 1

4. Quadratic Function
A function in which the greatest power of the variable is 2.
The graph of a quadratic function will be a U-shaped curve, called a parabola.
Ex: y = x y = 2x2 - 2x y = -2x2
The graph represents the quadratic function: y = -2x2
Axis of symmetry – vertical
line that passes through the vertex.
Vertex – turn around point.
Notice that the graph is opening downward.
This is because of the -2. Whenever the
coefficient of the x2 value is negative,
the graph of the quadratic function will
open down.
This makes the y-coordinate of the vertex the maximum of the graph!! x
-2x2 y
(x, y) -2
-2(-2)2 -8
(-2,-8) -1
-2(-1)2
(-1,-2)
-2(0)2
(0,0) 1
-2(1)2
(1,-2) 2
-2(2)2
(2,-8)
When graphing quadratic equations, you will form a table by substituting values for x into the function, and then plotting ordered pairs.

5. Graph the following quadratic functions…
y = 5x y = 3x y = -2x2 - 1 x
y = 5x2 y
(x, y) x
y = 3x2 +1 y
(x, y) x
y = -2x2 - 1 y
(x, y)

6. Formulas to keep in mind!!!
Slope = y2 – y1
x2 – x1
Slope-intercept: y = mx + b, where m = slope & b = y-intercept
Geometric Sequence: an = a1r (n – 1)
Arithmetic Sequence: an = a1 + (n – 1)d
Midpoint = x2 + x1 , y2 + y1
Review Surface Area formulas and Conversion

7. Practice Problems: What is the sum of the measures of <K and <L?
Zack conducted a survey in his school. He asked each student to choose his or her favorite subject. Zack wants to create a graph showing the percentage of students who chose each subject as their favorite.
Which type of graph would best represent these data?
47°
94 °
133 °
227 °
133 ° K L J
stem-and-leaf
circle graph
line graph
scatterplot

8. What is the slope of the line passing through the points (1, 3) and (5, 0)?
4. Rob would like to buy a $20 CD that is on sale for 15% off. He estimates that he will save at least $4.00.
*In your answer document, determine whether or not Rob’s estimate is reasonable. Show or explain how you decided if Rob’s estimate is reasonable.
- 4/3
- ¾
4/3

9. 6. What is the value of x when 3x < -2x + 15?
5. Evaluate: (23) (3-2).
6. What is the value of x when 3x < -2x + 15?
Kyle spins each spinner once and multiplies the two numbers he lands on.
What is the reasonable prediction for what might happen?
-36
- 6/6
8/9 72
X > 3
X < 3
X < 15
X > 15 3 2 5 6 2 4 5 1 3
The most likely product is 12.
The most likely product is 10.
The product cannot be less than 4.
The product cannot be greater than 18.