2.1 Quadratic Functions
This is the vertex of the function f(x) = x2 - 2x - 2
What is the point (1, -3)?
This is the end behavior of the graph of the function f(x) = -x(x - 1)5(x+2)
What is up on the left and down on the right?
The quotient of x³ - 6x² + 11x - 6 and x - 1
What is x² - 5x + 6?
How many positive and how many negative real zeroes might f(x) = x⁴ − x³ + x² + x − 1 have
What are 3 or 1 positive and 1 negative?
The final zero of a degree 23 polynomial with x = 1 with a multiplicity of 21 as a zero, and x = 5 + i as a zero
What is x = 5 - i?
These are the x-intercepts of the function f(x) = x2 - x - 42
What are the points (-7, 0) and (6, 0)?
This is the leading coefficient of the function f(x) = 2(3x - 4)(5x - 6)(7x - 8)
What is 210?
The quotient of x³ - 4x² + x + 5 and x - 2
(in the form f(x) + R/(x-2))
What is x² - 2x - 3 - 1/(x-2)?
The possible rational zeroes of f(x) = 12x⁹⁸⁷+24
What are
-24, -12, -8, -6, -4, -3, -5/2, -2, -3/2, -5/4, -1, -5/6, -3/4, -2/3, -1/2, -1/3, -1/4, -1/6, -1/12,
1/12, 1/6, 1/4, 1/3, 1/2, 2/3, 3/4, 5/6, 1, 5/4, 3/2, 2, 5/2, 3, 4, 6, 8, 12, 24
?
The zeroes of the function f(x) = x² + 17
What are x = i√17 and x = -i√17?
The vertex form of the function is f(x) = (x + 6)2 - 7
What is f(x) = x2 + 12x + 29?
This is the y-intercept of the function f(x) = (x + 16)²(x+4)
What is 1024?
This is f(2) for the function f(x) = x³ - 2x² - 5x + 6, without plugging into the equation (using the Remainder Theorem instead)
What is -4?
The zeroes of f(x) = x³ − 3x² + x + 1
What are x = 1, x = 1 + √2 and x = 1 − √2?
The zeroes of the function f(x) = x³ + 4x² + 5x
What are x = 0, x = -2 + i and x = -2 - i?
The expanded form of the function is f(x) = 6x2 - 144x + 1
What is f(x) = 6(x - 12)2 + 863?
This is the graph of the function f(x) = 7000x19(x + 800)2(x - 1)
What is a graph that goes down on the left and up on the right, bouncing off the x-axis at x = 800 and crossing through it at x = 0 and x = 1?
The fully factored form of f(x) = x⁴ - x³ - 7x² + x + 6
What is f(x) = (x - 1)(x + 1)(x + 2)(x - 3)?
The complete linear factorization of f(x) = 4x⁴ − 20x³ + 35x² − 25x + 6
What is f(x) = 4(x − 1)(x − 2)(x − 3/2)(x − 1/2)?
or f(x) = (x − 1)(x − 2)(2x − 3)(2x − 1)?
i³⁸⁵⁶⁹⁰¹ could only possibly be one of these
What is -i or i?
These are the x-intercepts of the function f(x) = x2 - 5x + 1
What are the points
((5+√21)/2, 0)
and
((5-√21)/2, 0)
?
This is the graph of the function f(x) = -(x + 100)²(x + 1)⁸x⁷(x - 1)⁹(x - 100)⁴
What is a graph that goes down on the left and right and bounces off the x-axis at x = -100 and x = -1 and x = 100, and crosses through the x-axis at x = 0, x = 1 and x = 100?
This is the quotient of x⁵ − 3x⁴ − 3x³ + 11x² + 2x − 8 and x² − 4
What is x³ − x² + x + 2?
The zeroes and multiplicities of each zero of the function f(x) = x⁵ − 2x⁴ − 2x³ + 8x² − 7x + 2
What are 1 with a multiplicity of 4 and 2 with a multiplicity of 1?
The expanded form of the function with zeroes x = -3 + i√7, x = -3 − i√7 and x = -9
What is f(x) = x³ + 15x² + 70x + 144?