Precalculus Chapter 2

1
Precalculus Chapter 2

• Polynomial Functions

Functions with powers that are WHOLE numbers
only!
2
Linear Quadratic Functions

• The degree of a polynomial function is the
  highest power and CANNOT be negative. Ex. Y
  1/x is NOT a polynomial function.
• Ex. The degree of y 2 x4 3x is _.
• The degree of a linear function is _ or _.
• The degree of a quadratic function is _ .

4
0
1
2
3
Linear Functions Slope

• Slope Rate of Change
• Ex. The COST function when ordering S class
  shirts costing 10 each with a shipping charge of
  20 is given by...
• __________________.

4
Linear Functions

• A long distance carrier offers a calling plan
  based on a monthly charge and a per minute RATE.
• Find the equation of the linear function with
  data points (100,8.95) and
  (250,14.95).

5
Linear Functions from DATA

• The correlation coefficient tells
• how well the regression equation fits the
  data.
• -1 lt r lt 1
• Positive or Negative ? Think slope.
• Positive r Agreement
• Negative r Disagreement

6
Quadratic Functions

• Standard Form Vertex Form
• y a ( x h )2 k
• The vertex is _at_ ( h , k ).
• The axis of symmetry is x h.
• If a gt 0, the parabola opens UP.
• If a lt 0, the parabola opens DOWN.

7
Quadratic Functions

• Find the vertex, axis of symmetry and direction
  of opening for the parabola with this equation

8
Quadratic Functions Completing the Square

• Find the vertex, axis of symmetry and direction
  of opening for the parabola with this equation

9
Writing a Quadratic Equationgiven the Vertex and
a Point

• Use Standard Form
• substituting the Vertex
• use an appropriate Stretch or Shrink.
• Use Standard Form
• substituting the Vertex and the pt in ( x , y
  ), and then solve for a.
• Use STAT EDIT to enter the Vertex and 2 points
  making use of the Axis of Symmetry. Then STAT
  CALC
• for a Quadratic Regression Equation.

10
Quadratic Functions

• Find the equation of the parabola with vertex ( 2
  , -5 ) and passing through the point ( 4 , 3 ).

11
Demand Revenue

• The demand equation is determined by the price.
• The higher the price, the
  _______ the quantity demanded.
• The lower the price, the
  _______ the quantity demanded.
• The Revenue function is the product price
  products R(x) x p

lower
higher
12
Modeling Predicting Demand

• Kelsie and Kompany sells c hundreds of their
  famous Kandy bars daily for p dollars according
  to the data in the table.
• Find the demand equation.
• Find the Revenue function.

See Examples 3 7
13
Craigs Catchers See Example 8

• Craig is training 8 year olds to be creative and
  cunning catchers in baseball.
• Craig knows s(t) -.5gt2 v0t s0 where s(t)
  is height, g 32 ft/sec2, v0 initial
  velocity and s0 initial height.
• Find the time it takes to catch the ball before
  hitting the ground when the ball is hit from a
  height of 3 feet with an initial velocity of 40
  feet/sec.