Graphs
How many x-intercepts can a quadratic have?
0, 1, or 2
What form is the polynomial f(x) = (2x - 3)(3x + 6)?
factored form
What are the zeroes of the function
f(x) = x(8 - 72x)?
0 and 1/9
Jason kicks a kickball as hard as he can. The height h, in feet, of the kickball until it reaches the ground is given by:
h(t) = t(- 7t + 49)
t is time, after the kickball is kicked. At what time does the kickball hit the ground?
t = 7
According to the Fundamental Theorem of Algebra, how many complex roots must a polynomial of degree 5 have?
5
(FTC states degree = number of complex roots)
Sketch a graph of a quadratic with two imaginary roots
Variety of correct answers.
What are the roots of the polynomial given
f(x) = (x - 3)(x + 6)?
x = 3 and x = -6
How many real zeroes does the function
f(x) = (x-5)(x+5)(x2+25) have?
only 2
The zeros are 5 and -5
Jason kicks a kickball as hard as he can. The height h, in feet, of the kickball until it reaches the ground is given by:
h(t) = t(- 7t + 49)
t is time, after the kickball is kicked. What are the zeros of the function?
0 and 7
According to the Fundamental Theorem of Algebra, if polynomial P has degree 12 and 8 real roots, how many non-real complex roots must P have?
4
(12 - 8 = 4)
What is the range of the function y=(x-3)^2 - 5
[-5, inf)
What are the zeroes of the polynomial below:
f(x) = (2x - 3)(3x + 6)?
x = 3/2 and x = -2
How many unique, real zeroes does the function
f(x) = (x2 +16)2(x+2)3(x-8)4 have?
only 2
(8 and -2)
Jason kicks a kickball as hard as he can. The height h, in feet, of the kickball until it reaches the ground is given by:
h(t) = t(- 7t + 49)
t is time, after the kickball is kicked. At what time is the ball at maximum height?
3.5
(7 divides by 2)
According to the Fundamental Theorem of Algebra, if polynomial P has degree 9 and 4 real roots, how many non-real complex roots must P have?
5
(9 - 4 = 5)
Sketch a graph of a cubic function with root 2 (double root) and -1.
answers will vary
Which is a factor of the polynomial f(x) = x2 - 5x + 6?
A. (x - 3)
B. (x+1)
C. (x + 6)
D. (x+2)
A. (x - 3)
Write a function f(x), with real zeroes of 5, -3, and 2/3.
Answers will vary , infinite possibilities
Jason kicks a kickball as hard as he can. The height h, in feet, of the kickball until it reaches the ground is given by:
h(t) = t(- 7t + 49)
t is time, after the kickball is kicked. What type of function does this represent?
Quadratic
According to the Rational Root Theorem, if polynomial P(x) = x3 - 2x2 + 5x - 2, how many possible real roots must P have?
4 possible roots
(-2, 2, -1, 1)
What it lowest possible degree of the given polynomial?
6
If 7 is a factor of polynomial p(x), which of the following must be true?
A. (x - 7) is a factor of p(x)
B. (x+7) is a factor of p(x)
C. p(0) = 7
D. p(x-7) = 0
A. (x-7) is a factor of p(x)
If 1/2 is a zero of polynomial p(x), which of the following must be true?
A. p(0) = 1/2
B. (x+1/2) is a factor of p(x)
C. p(1/2) = 0
D. p(x-1/2) = 0
C. p(1/2) = 0
Jason kicks a kickball as hard as he can. The height h, in feet, of the kickball until it reaches the ground is given by:
h(t) = t(- 7t + 49)
t is time, after the kickball is kicked. At what time does the kickball return to the ground?
x = 7
According to the Rational Root Theorem, if polynomial P(x) = 2x3 + 4x2 + 5x + 5, how many possible real roots must P have?
8 possible roots