Show:
Vertical & Horizontal Asymptotes
Synthetic Division
Sum & Difference of Perfect Cubes
Solving Multivariable Linear Systems of Equations
Finding the Equation of a Parabola that Passes through
Given Points
100
What is the process for finding vertical asymptotes?
Factor and cancel, if possible, and then set the denominator equal to zero and solve for x
100
In order to use synthetic division, the divisior must be in the form of what?
(x-k)
100
After un-cubing each term for the 1st factor:
Square the 1st, change the sign, take the product, always positive, square the last.
100
What method can be used in order to solve a multivariable linear system of equations?
Gaussian elimination
100
What is the standard form of a parabola?
y=ax^2+bx+c
200
What is the process for finding horizontal asymptotes?
If: numerator < denominator, then y=0 If: numerator = denominator, then y=(num. leading coeff.)/(denom. leading coeff.) If: numerator > denominator, then no horizontal asymptote present (slant asymptote present)
200
If the divisior is not in the form of (x-k), what other type of division could be used?
Long division
200
a^3-b^3=?
(a-b)(a^2+ab+b^2)
200
What are the Basic Row Operations?
1.) Interchange two rows 2.) Multiply one of the equations by a nonzero constant 3.) Add a multiple of one equation to another equation (elimination)
200
What is the first step to follow when trying to find the equation of a parabola that passes through given points?
Using the standard form of a parabola, substitute each point into the equation making three separate equations
300
If a horizontal asymptote is not present, how do you find the slant asymptote?
y=(top half of the rational function)/(bottom half of the rational function)
300
The quotient of synthetic division can sometimes be followed by what?
a remainder
300
a^3+b^3=?
(a+b)(a^2-ab+b^2)
300
What does it mean to be in Row-echelon form?
It means the systems have a "stair-step" pattern with leading coefficients of 1
300
What is the second step to follow when trying to find the equation of a parabola that passes through given points?
Simplify the three equations
400
Determine the vertical asymptote for the given rational function: f(x)=(x^2-x)/(x+1)
x= -1
400
Divide x^4+5x^3+6x^2-x-2 by x+2 using synthetic division
x^3+3x^2-1
400
Factor the given expression: 8x^3+125
(2x+5)(4x^2-10x+25)
400
What does it mean to be in Reduced Row-echelon form?
It means the systems have a diagonal of leading coefficients of 1 with all of the other coefficients being zeros
400
What is the final step to follow when trying to find the equation of a parabola that passes through given points?
Solve the system of equations using matrices or algebraically
500
Determine the vertical and horizontal asymptotes for the given rational function: f(x)=(3x^2+6x)/(x^2-x-6)
x=3 y=3
500
Divide 2x^4-5x^2-3 by x-2 using synthetic division
2x^3+4x^2+3x+6+(9/(x-2))
500
Factor the given expression: 2x^3-128
2(x-4)(x^2+4x+16)
500
Solve the given multivariable linear system of equations: x+y+z=2 -x+3y+2z=8 4x+y =4
Solution: (0,4,-2)
500
Find the equation of the parabola that passes through the given points: (-1,0), (1,4), and (2,-3)
y=-3x^2+2x+5