Quadratics
Factoring
Division
Graphing
Asymptotes
100
What form does a quadratic have when graphed?
What is a parabola?
100
Factor the quadratic f(x) = x^2 +4x - 32
f(x) = (x+8)(x-4)
100
Find the quotient and remainder by using long division: 8x^3 + 4x^2 -4x -3 by 4x+2.
Quotient: 2x^2 - 1 Remainder: -1
100
Roughly sketch what the graph of a quadratic where n is even and an is positive and describe end behavior.
As x approaches negative infinity, y approaches positive infinity and as x approaches positive infinity, y approaches positive infinity.
100
There are vertical and horizontal asymptotes... can your graph cross either of these?
Graph is allowed to cross horizontal but not vertical asymptotes.
200
f(x) = a(x-b)^2 + k
What is standard form?
200
Factor the quadratic f(x)= 2x^2 -5x -12
f(x)= (2x+3)(x-4)
200
Find the quotient and remainder using long division: x^6 - 5x^4 + x^2 -5 by x^2 - 5.
Quotient: x^4 + 1 Remainder: 0
200
Roughly sketch what the graph of a quadratic where n is odd and an is negative looks like and describe end behavior.
As x approaches neg infinity, y approaches pos infinity, and as x approaches pos infinity, y approaches neg infinity.
200
What is your HA if n<m?
y=0
300
Find the x and y intercepts of f(x)= -x^2 +8x - 7.
X-int: (1,0) and (7,0) Y-int: (0,-7)
300
Factor the quadratic 24x^2 - 22x - 35
(4x-7)(6x+5)
300
Divide x^5 + 3x^3 - 10 by x-1 and find quotient and remainder.
Quotient: x^4 + x^3 +4x^2 +4x +4 Remainder: 30
300
Factor and use the zeros to sketch a (rough) graph: P(x)= x^4 - 15x^2 - 16.
Zeros: 4, -4. Y-int: -16
300
How do you find vertical asymptotes?
VA occur wherever makes the denominator 0.
400
Express f(x) = 3x^2 + 6x + 4 in standard form.
f(x)= 3(x+1)^2 + 7
400
Factor the polynomial f(x)= 24x^3 - 6x^2 + 8x -2
(6x^2 +2)(4x-1)
400
Use synthetic division and the remainder theorem to evaluate P(c). P(x)= 3x^3 +22x^2 -2x +1 and c = 2/3
P(2/3)=31/3
400
Factor and find the zeros to help you sketch a (rough) graph of P(x) = x^4 - 4x^3 + 3x^2
Zeros: 0,0,3,1
400
Find asymptotes for (x^3 + 2x^2 - 4x +7)/(x-1).
VA: x = 1 HA: none because n>m
500
Find the max or min value for f(x)=2x^2 -20x +57
Max value = 7
500
Factor the polynomial f(x)=9x^3+36x^2-4x-16
(9x^2-4)(x+4)
500
Show that c = -2, 1/3 are zeros of P(x)= 3x^4 - x^3 - 21x^2 - 11x +6
Synthetic division shows that you get a remainder of 0 when using -2 and 1/3.
500
Factor and find zeros to help you sketch a (rough) graph of P(x) = x^3 - 3x^2 -10x. List domain and range.
Zeros: 0, -2, 5. Domain is all real numbers, range is all reals.
500
Find asymptotes of P(x) = (3x^2 + x - 10)/(x^2 +2x -8)
VA: x=-4, x=2 HA: y=3
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