Factoring Quadratics
Factor the following:
x2 + 4x + 4
(x + 2)(x + 2)
or (x + 2)2
What is the end behavior for y = x
x --> -∞, f(x) --> -∞
x --> ∞ , f(x) --> ∞
What are the roots to the function y = x2
x = 0
What are the roots/solutions/zeros of a function?
The x-intercepts
What is the discriminant for x2 + 5x + 4 = 0
b2 - 4ac a = 1, b = 5, c = 4
(5)2 - 4(1)(4)
25 - 16
= 9
Factor the following
x2 + 5x - 24
(x + 8)(x - 3)
What is the end behavior for y = x2
x --> -∞, f(x) --> ∞
x --> ∞ , f(x) --> ∞
What are the roots for the quadratic polynomial f(x) = -x2 + 2x + 3
x = -1, 3
A polynomial with one term
Monomial
What is the discriminant for 2x2 - x + 4 = 0
b2 - 4ac a = 2, b = -1, c = 4
(-1)2 - 4(2)(4)
1 - 32
= -31
Factor:
2x3 - 10x
2x(x2 - 5)
What is the end behavior for f(x) = x3 - 5x2 - x + 5
x --> -∞, f(x) --> -∞
x --> ∞ , f(x) --> ∞
What are the roots for f(x) = x3 + 2x2 - x - 2
x = -2, -2, 1
A polynomial with two terms
Binomial
Use the quadratic formula to solve for x:
0 = x2 + 2x + 1
x = -1
Factor
36x5 - 63x3
9x3(4x2 - 7)
What is the end behavior for f(x) = -x4 - 2x2 + x - 2
x --> -∞, f(x) --> -∞
x --> ∞ , f(x) --> -∞
The roots for f(x) = x5 + x - 3 are between which two consecutive integers?
The root is between x = 1 and x = 2
A polynomial with three terms
Trinomial
Use the quadratic formula to solve for x:
0 = x2 - 2x - 3
x = -1, x = 3
Factor
2x2 + 7x + 6
(2x + 3)(x + 2)
What is the end behavior for f(x) = 3x4 - 7x3 + 10x - 15
x --> -∞, f(x) --> ∞
x --> ∞ , f(x) --> ∞
The roots for f(x) = -x3 + 10x - 1 are between which two consecutive integers?
One root between x = -4 and x = -3
One root between x = 0 and x = 1
One root between x = 3 and x = 4
A polynomial with a highest degree of 2
Quadratic
Use the quadratic formula to solve for x:
0 = 3x2 + x - 5
x = -1.47, x = 1.14