Transcript of THIS IS 100 200 300 400 500 Chapter 2 Definitions Section 2-1Section 2-2Sections 2- 3/2-4 Sections...
THIS
IS
100 100 100 100 100 100
200 200 200 200 200 200
300 300 300 300 300 300
400 400 400 400 400 400
500 500 500 500 500 500
Chapter 2 Definitions
Section 2-1 Section 2-2 Sections 2-3/2-4
Sections 2-5/2-6
Section 2-7
If a polynomial P(x) has a squared factor such as (x-c)2,
then x=c is a…?
Definitions 100
Double Root
Defintions100
Any value of x for which P(x)=0 is a ____ of the equation?
Definitions 200
Root
Definitions 200
Linear and quadratic functions belong to a family of functions
known as…?
Definitions 300
Polynomial Functions
Definitions 300
The maximum or minimum values of the quadratic function
f(x)=ax2+bx+c occurs at…?
Definitions 400
-b/2a
Defintions 400
The following steps are for ________?
1.Start with the leading coefficient 2.Repeat the following until the last
coefficient is reached:a. Multiply by the value of xb. Add the next coefficient
Definitions 500
Synthetic Substitution
A 500
Classify the following polynomial function as linear, quadratic, cubic, quadratic, or quintic. Also, give its leading term, leading coefficient, and degree.
h(x)= 8-5x3
2-1100
Cubic;Leading term: -5x3
Leading coefficient: -5Degree: 3
2-1 100
State weather the function is a polynomial function. Give the zeroes of the function, if they
exist.X2-3x-4
____________
X2+1
2-1 200
It’s not a functionZeros: -1, 4
2-1 200
Find the value of the function (remember 1= ). Simplify the
answer.
h(x)=2x2-5x+6; h(1+i)
2-1 300
1-i
2-1 300
If P(x)= 3x3-7x2+2x+3, use synthetic substitution to find
P(-2/3)
2-1 400
-7/3
2-1 400
Find the value of the function (remember1= ). Simplify
the answer. x3-9x; ( )
2-1 500
2-1 500
Find the remainder when x5-2x3+x2-4
2-2 100
R=-4
2-2 100
Find the quotient and the remainder when the first
polynomial is divided by the second.
x3-2x2+5x+1; x-1
2-2 200
x2-x+4; R=5
2-2 200
Which of the following are factors of P(x)=x3-5x2+3x+9
a) x+2 b)x+3c) x-3
2-2 300
C
2-2 300
DAILY DOUBLE
2-2 400
DAILY DOUBLE
Place A Wager
Find the remaining roots2x4-9x3+2x2+9x-4=0;
Roots: x=-1, x=1
2-2 400
2-2 400
x=4; x=1/2
Find the quotient and the remainder when the first
polynomial is divided by the second.
x5+3x2+4; x2+2x+1
2-2 500
x3-2x2+3x-1;R=-x+5
2-2 500
If a polynomial P(x) is a squared factor such as (x-2)2, then x=c is a double root of P(x)=0. What can you infer about the graph?
2-3/2-4 100
It will be tangent to the x-axis (at x=c)
2-3/2-4 100
Sketch the graph of the equation y=(x+1)(x-2)(x-4)
2-3/2-4 200
2-3/2-4 200
Factor the polynomial function and sketch its graph
F(x)=x4-x2
2-3/2-4 300
2-3/2-4 300
Factor the polynomial function and sketch its graph F(x)= x4-2x3+2x-1
(Hint: x=1 is a triple root).
2-3/2-4 400
F(x)= (x-1)3(x+1)
2-3/2-4 400
A farmer wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other three
sides.
a)Express the area in terms of x and state the domain of the area function.
b) Find the value of x that gives the greatest area.
2-3/2-4 500
2-3/2-4 500
a) A(x)=-2x2+120x or x(120-2x)
D= 0<x<60
b) x=30
Solve x3-x2-5x+2=0 by using a graphing calculator.
2-5/2-6 100
x=-2, x=0.4, x=2.6
2-5/2-6 100
Solve x4-3x2=9 by using a graphing calculator.
2-5/2-6 200
2-5/2-6 200
X=-2.20, x=2.20
2-5/2-6 300
Solve x3+5x2-4x-20=0 by grouping.
2-5/2-6 300
x=2, x=-2, x=-5
Solve 2x4-x2-3=0 using the quadratic form.
2-5/2-6 400
X= ± i, ±
2-5/2-6 400
According to the rational root theorem, what are all the roots of
P(x)= 3x4+13x3+15x2-4=0 ?
2-5/2-6 500
x=-2 (double root), x=
2-5/2-6 500
Tell whether the following statement is true or false:
Some cubic equations have no real roots
2-7 100
False
2-7 100
Find the sum and product of the roots of the given equation:
4x2-3x+6=0
2-7 200
Sum: 3/4
Product: 3/2
2-7 200
Find a quadratic equation with roots 2±3i.
2-7 300
x2-4x+13=0
2-7 300
Find a cubic equation with integral coefficients that has the
given roots:
3 and 7-i
2-7 400
x3-17x2+92x-150=0
2-7 400
Find a cubic equation with integral coefficients that has no quadratic term and as one
of its roots.
2-7 500
x3-25x+66=0
2-7 500
The Final Jeopardy Category is:
Chapter 2
Please record your wager.
Click on screen to begin
Suppose you have 102 m of fencing to make two side-by-side rectangular
enclosures, as shown. What is the maximum area that you can enclose?