Steps for Factored Form
What's the first step when sketching the graph of a factored form polynomial?
Find end behavior
What's the first step when sketching the graph of a standard form polynomial?
Find end behavior
How do you find degree of a standard form polynomial?
Highest exponent
If the multiplicity of a factor is odd, what will happen at the x axis at that x-intercept?
The graph will bounce the x axis.
What is a constant?
A number without a variable
What's the second step when sketching the graph of a factored form polynomial?
Find x-intercepts
What's the second step when sketching the graph of a standard form polynomial?
Find y intercept
How do you find leading coefficient of a standard form polynomial?
Coefficient of biggest degree term
If the multiplicity of a factor is even, what will happen at the x axis at that x-intercept?
The graph will bounce the x-axis.
How do you find the y-intercept of a standard form polynomial?
1. Find the constant
2. Make point (0,y)
What's the third step when sketching the graph of a factored form polynomial?
Find multiplicities
What's the third step when sketching the graph of a standard form polynomial?
Estimate x-intercepts on a calculator
How do you find degree of a factored form polynomial?
Add all exponents of variables
Given that f(x) = (x-3)4(x+3)5, what will happen to the graph at the x-axis at the point (3, 0)? Give the multiplicity of the factor needed to answer this question for extra bonus points.
The graph will bounce the x-axis at (3,0) because the multiplicity of the factor (x-3) is 4 which is even.
How do you find the y-intercept of a factored form polynomial?
1. Set all x to 0
2. Solve for y
3. Make point: (0,y)
What's the fourth step when sketching the graph of a factored form polynomial?
Find y-intercept
Describe in detail the fourth step of sketching a standard form polynomial.
Sketch! Draw points and arrows for end behavior, but then you can use a calculator
How do you find leading coefficient of a factored form polynomial?
Multiply the front coefficient by all coefficients of x terms
What type of number should you look for when finding the multiplicity of a factor? (Coefficient, variable, exponent, constant, even numbers, odd numbers, etc.)
The exponent of the factor
What is the y-intercept of the polynomial y=3x4+2x-1?
(0,-1)
Describe in detail the 5th step of sketching a factored form polynomial.
2. Draw arrows for end behavior
3. Connect the dots using bounce and cross
True or False? You still need to find your multiplicities when sketching the graph of a standard form polynomial.
FALSE
What is the leading coefficient of the polynomial y = 3x7(-x+2)(2x-1)2(x-3)5.
3 * -1 * 2 * 2 * 1 * 1 * 1 * 1 * 1 = -12
What are the steps for finding the x-intercepts of a factored form polynomial?
1. Set all factors = 0
2. Solve for each x.
3. Make points (x,0)
What is the y-intercept of the polynomial y=3(x-1)(x+1)2(x-2)?
(0,6)