General Shape
Give 2 examples of an even degree function and 2 examples if an odd degree function.
Answers will vary ex. Even: x2, x4, x10, x24 or Odd: x, x3, x5, x13
How do you solve for the x intercepts? How do you solve for the y intercept?
In order to solve for the x intercepts you must factor the equation and set it equal to zero. In order to find the y intercept you set x = 0 and substitute it in and then solve for y.
What are the steps for sketching a graph for polynomials?
1. Find the general shape, 2. Find x and y intercepts, 3. Fill in the rest
Describe what would happen to the graph of an Odd degree function if it is positive or if it is negative.
If it is positive the end behavior should have the left end pointing down and the right end pointing up. If it is negative the left end should be pointing up and the right end should be pointing down.
Find the x intercept for y=x2-4x+3
(1, 0), (3, 0)
How do you find the number of turning points?
Subtract 1 from the highest degree of the polynomial.
How many turning points are in this function: x4 + 3x3 - 4x2 - x + 12 ?
3 turning points
Find the y intercept for y=-x3-3x2+x+3
(0, 3)
What is a multiplicity and how does it affect the graph?
Multiplicity is when you have multiple of the same x intercept. It affects the graph by instead crossing through the x-axis at that point it bounces off at that point.
Determine the end behavior or the function: -x2+3x - 10
Both ends point down
Find the x and y intercept for y=(x-1)(x+2)(x-3)
x intercepts: (-2, 0), (1, 0), (3, 0)
y intercept: (0, 6)
Find the x and y intercepts, the end behavior, and shape for f(x) = x2-5x+4
x intercepts: (1, 0), (0, 4)
y intercept: (4, 0)
Shape: even degree function with 1 turning point
End Behavior: positive with both ends pointing up
Determine the general shape of the function (odd or even, positive or negative, end behavior): -x3+2x2-3
Odd degree function, negative, first end pointing up second one pointing down.
Find the x and y intercepts for y = 2(x-1)(x+2)(x-3)
x intercepts: (1, 0), (-2, 0), (3, 0)
y intercept: (0, 12)
Find the multiplicity for y = -(x+2)(x-3)(x+5)(x+2)
x=-2 multiplicity of 2