Graphs of Polynomial Functions. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

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Polynomial Functions and Graphs

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Presentation transcript:

Graphs of Polynomial Functions

Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

Click on the graph below to connect to an interactive page.

Turning Point – Point on the graph such that the value of the function is a relative maximum or a relative minimum. A graph of a polynomial of degree n can have as many as n-1 relative extrema. Leading Coefficient – coefficient of term with the highest degree. If a is positive, and If n is even, both left and right sides of the graph . If n is odd, the left side , and the right side . If a is negative, and If n is even, both left and right sides of the graph . If n is odd, the left side  and the right side . degree

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EVEN function : f(  x) =f(x) ; symmetric about the y-axis. ODD function: f(  x)=  f(x) ; symmetric about the origin. even odd How many relative extrema does each graph have?

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What is the equation of the graph? 1 st : the shape is cubic and positive The factors are (x+1), x and (x-2). So, the equation must be : 2nd : there are zeros at –1, 0 and 2   How many relative extrema?

What is the equation of the graph?

What is the shape of the graph of an even polynomial equation with a degree of 4, a negative leading coefficient and 2 distinct real zeros?

What is the shape of the graph of the polynomial equation of degree 5 with a positive leading coefficient and 5 distinct real zeros?

Graph without a calculator:

**If (x-r) is a factor k times, then r is a zero of multiplicity k. That zero is a touch point (point of tangency) if its multiplicity is an even number. (It will not cross the x-axis at that point.) Graph: If the multiplicity is odd and > 1, the graph will flatten out as it crosses the x-axis.

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