Below you are given a picture of a quadratic, you must label the parts of the quadratic that have an arrow pointing to them.
What is the Lead Coefficient and Degree of the following polynomial:
y=x8+2x7+3x6+4x5+5x4+6x3
Degree: 8
Lead Coefficient: 1
By the Fundamental Theorem of Algebra, how many roots should the following equation have?
y=x10-x4-5x3+11x11-1
11, because the highest degree that the equation has is 11!
Find the horizontal asymptote of the following rational function:
y=3x2+4x+24x-1
there is no horizontal asymptote!
Convert the following Standard form Equation into its Factored form Equation
y=x2-10x-24
y=(x-12)(x+2)
Given the graph above, list the end behavior of the graph as:
x approaches infinity, f(x) approaches ____________
x approaches negative infinity, f(x) approaches ________
x approaches infinity, f(x) approaches infinity
x approaches negative infinity, f(x) approaches
negative infinity
Using the Fundamental Theorem of Algebra, how many real roots and imgainary roots does this function have?
2 imaginary and 0 real, because the graph never touches the x axis
Find the horizontal asymptote of the following rational function:
g(x)=2x+3x2-13x+4-3x2
y = -1
Convert the following equation from Standard form to Vertex form:
y=x2-10x+16
y=(x-5)2-9
Given the function, list the zeros of the function, and their multiplicities
g(x)=x(x-3)5(x+3)(x+4)2
Zero at 0, with multiplicity 1
Zero at 3, with multiplicity 5
Zero at -3, with multiplicity 1
Zero at -4, with multiplicity 2
-√34+4,567i
Find the Conjugate of the following term
-√34-4,567i
Factor the following rational function:
y=(x2+12x+36)x2-3x-28
f(x)=(x+6)(x+6)(x-7)(x+4)
Write the equation of the line (in any 3 forms)
Standard form:
y=x2-8x+12
Factored form:
y=(x-2)(x-6)
Vertex form:
y=(x-4)2-4
Given the graph below, write the equation to this graph in factored form
(x+3)(x+1)(x-4)
(-3+5i)(-3-5i)
Simplify the following terms by multiplication
34
y=(x+4)(x-3)(x+4)(x-4)
List any vertical asymptotes the rational function has:
There is a vertical asymptotes at x = 4
y=2x2+12x+12
Convert the following equation from Standard form to Vertex form
y=2(x+3)2-6
Given the equation below, list the end behaviors of the graph:
as x approaches infinity, f(x) approaches _______
as x approaches negative infinity, f(x) approaches______
R(t)=−0.037t4+1.414t3−19.777t2+118.696t−205.332
a negative lead coefficient and an even degree means:
as x approaches infinity, f(x) approaches negative infinity
as x approaches negative infinity, f(x) approaches negative infinity
Find the complex roots of the following quadratic:
T(x)=x2+4x+5
-2+iand-2-i
List any zeros the rational function has:
y=(x+5)(x-4)(x-3)(x-4)
There is a zero at (-5,0)