That's a Fact(or)
When written in factored form, f(x)=-3x2-33x-72 looks like this.
What is f(x)=-3(x+3)(x+8)
These are also called zeros, roots, or solutions.
What are x-intercepts?
This is the axis of symmetry of f(x), when f(x)=-3(x+8)2-27.
What is x=-8?
In y=6x2-3x+7, the vertex is a __________.
What is a minimum?
This is the y-intercept of the rational function r(x).
What is (0,0)?
These are the factors of 3x2-10=x.
What are (3x+5) and (x-2)?
These are the three ways to solve a quadratic function to find its zeros.
What are factoring, the square-root property, and the quadratic formula?
Given f(x)=6x2-36x+30, the vertex is ______.
What is (3,-24)?
In y=-2x3-5x6+x9-2x2+7x-3, the right end of the graph does this.
What is rises?
These are the x-intercepts of the rational function r(x).
What are (0,0) and (-3,0)?
This is the factored form of a degree 7 polynomial with leading coefficient of 3 and zeros of 2, 0 (multiplicity 3), -6 (multiplicity 2), and -7.
What is f(x)=3x3(x-2)(x+6)2(x+7)?
The shortcut to find the x-intercepts of a rational function is to set ______________________ equal to zero.
What is the numerator?
You run a side business selling birthday cakes from your home. Your monthly profit P from selling x cakes is found by P(x)=-x2+14x+406. This is your maximum monthly profit.
What is $455?
If the graph of a polynomial crosses the x-axis, then the multiplicity of that zero is ________.
What is odd?
This is the Horizontal Asymptote of the rational function r(x).
What is y=2?
When completely factored, y=-2x4-10x3+12x2 looks like this.
What is y=-2x2(x-1)(x+6)?
If (x-c)k is a factor of f(x), then c is a zero of f(x) with __________________.
What is multiplicity of k?
This is the result when x4-11x2+2x+17 is divided by x-3.
What is x3+3x2-2x-4+5/(x-3)?
If a rational function is graphed with an asymptote at x=-3, then it must be a ________ asymptote.
What is vertical?
These are the Vertical Asymptotes of the rational function r(x).
What are x=-3 and x=3?
This is the COMPLETE factorization of g(x)=x3-11x2+8x+20 given that (x+1) is a factor of g(x).
What is g(x)=(x+1)(x-2)(x-10)?
All possible rational zeros of a polynomial can be found by finding all combinations of the factors of the __________________ over the factors of the ________________________________________.(Must include both answers in order.)
What are constant and leading coefficient?
These are all of the possible rational zeros of f(x)=2x4+3x2-16.
What are +-1, +-2, +-4, +-8, +-16, +-1/2?
In a polynomial whose degree is odd, if the LEFT end falls, the leading coefficient must be _________.
What is positive?
This is the domain of the rational function r(x).
What is (-inf,-3)u(-3,3)u(3,inf)?