Polynomial, Power, and Rational Functions

1
Polynomial, Power, and Rational Functions

• Chapter 2

2
Linear and Quadratic Functions and Modeling

• 2.1

3
Polynomial
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
Is the Function a Polynomial?

• 2,4,6

8
Linear Function

• Find the slope or the average rate of change
• Change in y over change in x.
• Rise over run

9
Linear Function, Example

• Find the Equation of a Linear Function
• 8

10
Standard Form
11
(No Transcript)
12
Remember that x and y intercepts can help you
decide which graph is the graph of the given
quadratic function.
13
Examples14,16,18
14
(No Transcript)
15
Quadratic Function

• State the transformations applied to x2 to get
  the current quadratic
• Completing the Square to see the
  transformationscreating vertex form
• Example--20

16
Using Completing the Square to Rewrite a
Quadratic Function in Vertex Form

• Put y or f(x) on the left side of the equation
  and all other terms on the other side of the
  equation. Simplify the right side if needed.
• Y3x25x-4 want to rewrite as
• Y a(x-h)2 k

17
Using Completing the Square to Rewrite a
Quadratic Function in Vertex Form

• Factor out the coefficient of the x2 term, a,
  unless it is one, from all the terms with x on
  the right side of the equation.
• Y3(x25/3x)-4
• Y a(x-h)2 k
• Divide the coefficient of the x term by two and
  then square the result.
• (5/3)/2 5/6 (5/6)225/36

18
Using Completing the Square to Rewrite a
Quadratic Function in Vertex Form

• Add the resulting number to the term in the
  parenthesis. Then subtract a times the amount
  added from the constant term.
• Y3(x25/3x25/36)-4-325/36
• Y a(x-h)2 k

19
Using Completing the Square to Rewrite a
Quadratic Function in Vertex Form

• Factor the quadratic part and simplify the
  constant part.
• Y3(x 5/6)2-73/12
• Y a(x-h)2 k

20
Write an Equation for the Parabola

• 40

21
Modeling

• Enter and plot the data as a scatter plot.
• Find the regression model that best fits the
  problem situation.
• Superimpose the graph of the regression model on
  the scatter plot, and observe the fit.
• Use the regression model to make the predictions
  called for in the problem.

22
Linear Modeling

• If the scatter points look like they are
  clustered along a line, then they have a linear
  correlation.
• Positive linear correlationpositive slope
• Negative linear correlationnegative slope
• r correlation coefficientmeasures the strength
  and direction of the linear correlation of the
  data set.

23
Linear Correlation Coefficient Properties

• -1,1
• rgt0 there is a positive linear correlation
• rlt0 there is a positive linear correlation
• r1, then there is a strong linear correlation.
• r0, there is a weak or no linear correlation

24
Quadratic Modeling

• Finding maximums and minimums
• Calculator
• Use max/min function
• By hand
• Find the vertex and determine if it is a max or a
  min by determining which way the graph points.

25
Quadratic Modeling

• Creating Vertical Free-Fall Motion equations.
• S(t) -1/2 gt2 votso
• v(t) - gt vo
• t is time, g32ft/s2 or 9.8m/s2 is the
  acceleration due to gravity.
• Initial heightso
• Initial velocity--vo

26
Quadratic Modeling Example

• 62