?v=cqj5Qvxd5MO Linear and Quadratic Functions and Modeling

A polynomial function is a function of the form: All of these coefficients are real numbers the exponent must be a nonnegative integer Remember integers are … –2, -1, 0, 1, 2 … (no decimals or fractions) so nonnegative integers would be 0, 1, 2 … The degree of the polynomial is the largest power on any x term in the polynomial.

Not a polynomial because of the square root since the power is NOT an integer Determine which of the following are polynomial functions. If the function is a polynomial, state its degree. A polynomial of degree 4. A polynomial of degree 0. We can write in an x 0 since this = 1. Not a polynomial because of the x in the denominator since the power is NOT nonnegative x 0

Graphs of polynomials are smooth and continuous. No sharp corners or cusps No gaps or holes---it can be drawn without lifting pencil from paper This IS the graph of a polynomial This IS NOT the graph of a polynomial

POLYNOMIAL FUNCTIONS OF NO AND LOW DEGREE NAME FORM DEGREE Zero function f(x) = 0 Undefined Constant function f(x) =a 0 Linear function f(x) ax + b 1 Quadratic function f(x) = ax² +bx + c 2 a ≠ 0

LINEAR EQUATIONS

If we look at any points on this line we see that they all have a y coordinate of 3 and the x coordinate varies. (-4, 3) (-1, 3) (2, 3) Let's choose the points (-4, 3) and (2, 3) and compute the slope. This makes sense because as you go from left to right on the line, you are not rising or falling (so zero slope). The equation of this line is y = 3 since y is 3 everywhere along the line. In general, the equation of a horizontal line is y = b, where b is the y coordinate of any point on the line.

To find the average rate of change of a function between any two points on its graph, we calculate the slope of the line containing the two points. (7, 8) (0, 0) So the average rate of change of this function between the points (0, 0) and (7, 8) is 8/7 To find the average rate of change of a function between any two points on its graph, we calculate the slope of the line containing the two points. Slope of this line

S C A T T E R D I A G R A M S LINEAR CURVE FITTING A scatter diagram is a plot of ordered pairs generally obtained by observation of some relation.

Look at these scatter diagrams to see if the relation looks linear or nonlinear. LINEAR NONLINEAR LINEAR NONLINEAR LINEARNONLINEAR

Let's look at some data gathered about the relationship between the speed of a certain car and the miles per gallon it gets speed x MPG y ordered pair (x, y) We can plot these points and see if it looks like there is a relationship It looks like a linear relationship because as you look it seems to have the pattern of a line with negative slope

We could come up with a function to estimate the miles per gallon given the speed. We'll pick two points on or near the line we made and find the slope and then use the point-slope formula. We'll choose (52, 28) and (65, 17) (52, 28) (65, 17) Find the estimated MPG if the car speed is 70 mph mpg

Click here Click here for help on how to use your calculator to create a scatter diagram and find the line of best fit. We could each come up with a slightly different line if we picked two different points to use. There is a process for finding the best line. This process is covered in a statistics class. We'll just use the calculator to find what is called the "line of best fit".

Properties of the Correlation Coefficient, r ≤ 1 2. When r > 0, there is a positive linear correlation 3. When r < 0, there is a negative linear correlation 4. When | r | ≈ 0, there is weak or no linear correlation.