Transformations/Even or Odd?
State the parent function: 4x3
x3
What are the zeros of (x-2)(x+3)=0
x=2, x=-3
My polynomial has 4 as a zero. What is one of its factors?
(x-4)
How does f(x) = x3+5 transform the parent function?
Translates up 5
Find the zeros of x2-2x-8
4, 2
Is x - 3 a factor of P(x) = x3-4x2+x+6? If so, write P(x) as a product of two factors.
Yes, (x - 3) (x2 -x -2)
If the zeros on the graph are x = 2 and x = 3, what are the factors of the function?
(x-2) and (x-3)
Describe the transformations from f(x) = x3 to g(x) = -2(x-1)3+5
Reflection over x-axis, right 1, up 5, vertical stretch by a factor of 2
Factor completely: 3x3 - 9x2 + 6
3x(x-1)(x-2)
If f(x)=x3−6x2+5x+12 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
x= -1, 3, 4
Find the zeros of the function f (x ) = x3 - 5x2 + 7x - 3, and describe the behavior of the graph at each zero. (crosses or touches)
x=1: multiplicity 2 → graph touches x-axis
x=3 multiplicity 1 → graph crosses x-axis
Is f(x) = 5x3 - x even, odd, or neither?
Odd
Factor and find the zeros: 2x3-3x2-18x+27
x=3, -3, and 3/2
If f(x)=x3−4x2−19x−14 and f(−1)=0, then find all of the zeros of f(x) algebraically.
-1, 7, -2
Sketch the graph by finding the zeros and list the zeros: x3 - 3x2
x= 0, x = 3
Is f(x) = x4-3x2+1 even, odd, or neither?
Neither
If the zeros are x = 1, 5, and 2, what is the equation in standard form?
x3-8x2+17x-10
Find all real and imaginary solutions to the equation. x3−4x2+4x−16=0
2i, -2i, 4
If the zeros are x = 1, 2, 0, and 3 what is the equation in standard form?
x4-6x3+11x2-6x