Download Ex. 3x5 + 6x4 - 2x3 + x2 + 7x - 6 degree: coefficients: leading

3.2 Polynomial Functions and their Graphs
Ex. 3x5 + 6x4 - 2x3 + x2 + 7x - 6
degree:
coefficients:
leading coefficient:
constant:
Monomial: 1 term; 2x
Binomial: 2 terms; 3x + 4
Trinomial: 3 terms; 4x2 + 3x + 6
The graph of a polynomial function is continuous. It has
no holes or breaks. It is a smooth curve with no
corners or sharp points (cusps).
End Behavior:
If the largest exponent is even:
Use x2 as an example.
If the largest exponent is odd:
Use x3 as an example.
Zeros of Polynomials
What does it mean to be a zero of a polynomial?
1. x = c is a root of the
equation, so P(c) = 0.
2. x - c is a factor of P(x).
Ex. P(x) = x2 +x - 6
Multiplicity of a Root
The multiplicity of a root is the same as the exponent on the
factor.
f(x) = x2
If the multiplicity is even, it "bounces" off the axis.
f(x) = x3
If the multiplicity is odd, it goes through the axis.
Ex. Sketch the graph of the polynomial function.
P(x) = (x + 2)(x - 1)(x - 3)
Ex. Graph the function. Make sure it exhibits the correct
intercepts and end behavior.
P(x) = x3 - 2x2 -3x
P(x) = -(x+3)2(x-1)3
P(x) = x4 - 3x3 + 2x2
P(x) = x3 + 2x2 - 4x - 8
Local Extrema of Polynomials
If P(x) is a polynomial of degree n, then the graph of
P has at most n-1 local extrema.
Determine how many local extrema each polynomial has.
Set window at :x = -5,5 y = -100,100
1. P(x) = x4 + x3 -16x2 -4x + 48
2. P(x) = x5 + 3x4 -5x3 -15x2 +4x - 15
3. P(x) = 7x4 + 3x2 -10x
Warm­Up Test Review 12/17/14
1. Find x. Round to the nearest tenth.
2. Solve for the missing angle.
Round to the nearest tenth.
3. Solve the triangle. Round answers to the nearest tenth.
4. Find x and y. Round answers to the nearest tenth. 5. Then find the area.