Section 2-1 Linear and Quadratic Functions

Section 2-1 polynomial functions polynomial functions linear functions linear functions rate of change rate of change linear correlation linear correlation quadratic functions quadratic functions vertical motion problems vertical motion problems

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

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

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

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

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 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 > 0 (same for negative and r 0 (same for negative and r < 0) if r is near 1 then there is strong correlation and near 0 is weak or no correlation if r is near 1 then there is strong correlation and near 0 is weak or no correlation

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

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

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

Vertical Motion there is a linear equation which can track the vertical velocity of the object at a given time 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) 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)