Linear and Quadratic Functions

1
Section 2-1

• Linear and Quadratic Functions

2
Section 2-1

• polynomial functions
• linear functions
• rate of change
• linear correlation
• quadratic functions
• vertical motion problems

3
Polynomial Functions

• the only operations on the variable are mult.,
  addition, and subtraction
• examples of poly.s

4
Polynomial Functions

• functions which are not polynomials
• variable under a square root
• variable in an exponent
• variable in a denominator
• variable with a negative exponent

5
Linear Functions

• in the form
• m is the slope and b is the y-intercept
• linear functions have degree 1
• problems might involve the use of the slope
  formula, slope-intercept form, and point-slope
  form

6
Rate of Change

• the average rate of change between two values (x
  a and x b) is given by the following
  equation
• for a linear function, the average rate of
  change is constant (the slope) and the initial
  value is the y-intercept

7
Linear Correlation

• when points of a scatter plot are clustered
  around a line we say there is a linear
  correlation between the quantities represented
  by the data
• if the regression line has positive slope then
  there is a positive correlation and r gt 0 (same
  for negative and r lt 0)
• if r is near 1 then there is strong correlation
  and near 0 is weak or no correlation

8
Quadratic Functions

• the graph of a quadratic function is called a
  parabola
• graphs can be sketched using the normal
  transformations if the equation is written in
  vertex form

9
Quadratic Functions

• if the equation is in standard form then finding
  the vertex takes a little work
• to convert from standard form to vertex form you
  must complete the square

10
Vertical Motion

• a special quadratic equation is used to track
  the height of an object (that is moving
  vertically) versus time
• g is the force due to gravity and which value
  you use depends on the units

11
Vertical Motion

• there is a linear equation which can track the
  vertical velocity of the object at a given time
• you can use these functions to find out the
  maximum height the object can reach, when it hits
  the ground, or its velocity when it hits the
  ground (or other things as well)