Synthetic Division
When doing synthetic division, the last number can be either a zero or a number. Regardless what is that called?
Remainder
This transformation occurs to the graph of f(x) = x3 to create the graph of g(x) = x3 - 5.
5 units down OR vertical shift/translation
For the polynomial f(x) = 7x3 - 2x5 + x - 9, this is the leading coefficient.
-2
The highest power is 5
A model for the number of people, P, at a park t hours after it opens is P(t) = 5t2 + 10t + 3. This is the number of people in the park exactly 2 hours after it opens. YOU MUST INCLUDE UNITS
Hint: Find P(2)
43 people
Name one of the former US capital cities before Washington DC in 1800.
Philadelphia, PA; New York, NY
Annapolis, MD; Lancaster, PA; Princeton, NJ; Trenton, NJ; Baltimore, MD
Given the divisor is (x+4), what is the k value that you multiple the outside numbers by in synthetic division.
-4
Remember do the opposite in the room with x
The transformation f(x) to -f(x) causes the graph of the polynomial to do this.
Reflection across the x-axis
This is the end behavior of the graph of f(x) = -4x4 + 3x3 - 1.
Right (DOWN) and Left (DOWN)
The model h(t) = -16t2 + 80t + 2 describes the height h of a rocket t seconds after launch. What is my initial height?
2 units because the y-intersect is at (0,2)
This element, with the atomic symbol Fe, is the primary component of steel and is essential for carrying oxygen in your blood.
Iron
Given (x3 + 2x - 7) ÷(x - 1), x2 term is missing so what do you put as a placeholder?
0 zero
If you do not see the power then it is zero
These two transformations, in order, change the parent function f(x) = x4 into g(x) = (x+2)4 + 7.
Horizontal shift 2 units left and a vertical shift 7 units up
A polynomial has real roots at x = -2 (multiplicity 1), x = 0 (multiplicity 2), and x = 5 (multiplicity 1). This is the lowest possible degree the polynomial can have.
Hint: Each multiplicity is a degree
4 (Because 1 + 2 + 1 = 4)
When analyzing a data table, you find that the fourth differences of the y-values are constant and non-zero. This is the type of polynomial function that should be used to model the data using the calculator's Regression feature.
A quartic (or 4th degree) function
What US city's name translates to “the meadows” in Spanish
Las Vegas, NV
Given that (x - 3) is a factor of the polynomial P(x) = x3 - 6x2 - x + 30, these are the other two linear factors. Provide the zeros including x=3
x=3
x=-2
x=5
Name the THREE transformation of the parent function that was applied to: f(x) = x3 -> g(x) = -3(x-1)3
Reflection on the x-axis
Vertical stretch by a factor of 3
Shift 1 unit right
This is the key difference in the behavior of a graph at a root with an odd multiplicity (like 1 or 3) compared to a root with an even multiplicity (like 2 or 4).
It is guaranteed that an odd-degree polynomial will cross the x-axis cause the end behavior is opposite on the right and left side, while an even-degree polynomial may or may not cross the x-axis depending on the specific function.
The profit, P, for selling x T-shirts is modeled by P(x) = -0.5(x-20)(x-150). According to this model, these are the two "break-even" points (where profit is $0).
selling 20 T-shirts and selling 150 T-shirts
Nevada is the largest producer of this precious metal in the United States, accounting for over 75% of all U.S. production
Gold
P(x) = 4x3 - 8x2 + 5x - 5 is divided by (2x - 3). Use synthetic division to find the quotient and any remainder if any
4x^2-2x+2 -2/(2x-3)
The graph of a cubic function has its point of inflection at (4, -2) and passes through the point (5, 1). This is the full equation for the function in the form y = a(x-h)3 + k.
h=4 , k=-2, x=5, y=1 find a
y = a(x-h)3 + k
y = 3(x-4)3 - 2
This is the specific equation of a cubic polynomial in factored form that has roots at x = -4 and x = 1 (with a multiplicity of 2 for both roots), and also passes through the point (2, 6).
f(x) = (1/6)(x+4)2(x-1)2
The profit P (in thousands of dollars) for a new product t months after its launch is modeled by the function P(t) = t3 - 10t2 + 31t - 30. Given that the company "breaks even" (has $0 profit) at t=2 months, these are the two other times when the profit is also $0. Hint: Polyn Root Finder
3 months and 5 months
What common item was originally sold by Amazon as its only product?
Books