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How do you find the x-coordinate of the parabola
f(x)=(ax^2)+bx+c
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How do you find the x-coordinate of the parabola
f(x)=-a-bx+(cx^2)
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How do you move this parabola "a" units up?
f(x)=x^2
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How do you move this parabola "a" units down?
f(x)=x^2
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How do you move this parabola "a" units Left?
f(x)=x^2
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How do you move this parabola "a" units Right?
f(x)=x^2
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How do you stretch this parabola "a" units?
f(x)=x^2
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Definition
f(x)=a(x^2)
Place the point, not the vertex on "a".
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What is the degree of a polynomial function?
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Definition
The largest exponent
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What is the leading term of this function?
f(x)=((Ax^b)+(Cx^d))/E
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Definition
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What is the leading coefficient of the function?
f(x)=((Ax^b)+(Cx^d))/E
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When is the graph a W shape?
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Definition
The degree is even and the leading coefficient is positive
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When is the graph an upside down W shape?
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Definition
The degree is even and the leading coefficient is negative
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When the graph is a S shape?
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Definition
The degree is odd and the leading coefficient is positive
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When the graph is a S shape reflected over the y-axis?
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Definition
The degree is odd and the leading coefficient is negative
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What is the y-intercept of this polynomial function?
(Ax^3)+(Bx^2)+Cx+D
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How do you describe the end behavior of this polynomial function?
-Ax^b(x+C)
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Definition
1.) Distribute
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2.) Now determine the shape using what you know about end behaviors.
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What are the x-intercepts of this polynomial function?
-Ax^b(x+C)
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Definition
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What is the multiplicity of a zero?
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The degree of the factor the zero originates from
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When does the graph at the zero touch the x-axis?
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Definition
When the multiplicity is even
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When does the graph at the zero cross the x-axis?
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Definition
When the multiplicity is odd
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What are the intervals that can be tested for this polynomial function?
-Ax^b(x+C)
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Definition
(-Infinity,-c)U(-c,0)U(0,Infinity)
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How do you find what intervals are below and above the x-axis?
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Definition
Choose a number from the interval, insert that number into the function, if it yields a negative result then that interval falls below the x-axis, and if not then that interval is above the x-axis.
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How do you find the y-intercept of this polynomial function?
-Ax^b(x+C)
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Definition
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If f(-x)=f(x), then the graph of f is symmetrical about what axis?
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Definition
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If f(-x)=-f(x), then the graph symmetrical about what?
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How do you determine the maximum number of turning points?
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Definition
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What is the degree of this polynomial?
-Ax^b(x+C)
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Definition
Distribute the polynomial, and then the degree is the highest exponent
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Where is this graph above the x-axis?
f(x)=x(x+a)(x-a)(x+b)
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Definition
(-Infinity,-b)U(-a,0)U(a,Infinity)
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What are the real zeroes of this function?
f(x)=x(x+a)(x-a)(x+b)
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Definition
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All the zeroes of this function cross or touch the x-axis?
f(x)=x(x+a)(x-a)(x+b)
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Definition
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Where is this graph below the x-axis?
f(x)=x(x+a)(x-a)(x+b)
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Definition
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What is the y-intercept of this function?
f(x)=x(x+a)(x-a)(x+b)
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Definition
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What are the symmetries of this function?
f(x)=x(x+a)(x-a)(x+b)
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Definition
There are no symmetries
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How do you list the possible rational zeros of a polynomial function?
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Definition
(Factors of the Constant/Factors of Leading Term)
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How do you test a possible zero, to verify if it is a rational zero?
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Definition
Use the conjugate of the rational zero in synthetic division, dividing it with the polynomial, if the remainder is a zero, then the possible zero is a rational zero.
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What do you do if after using synthetic division to test a possible zero, it turns out to be a rational zero, and you now have a quadratic function?
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Definition
Use the quadratic formula to find the remaining rational zeroes.
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What do you do if after using synthetic division to test a possible zero, it turns out to be a rational zero, and you do not have a quadratic function?
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Definition
Test another possible zero, until you find another rational zero, one that generates a quadratic function.
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What is the domain of this function?
A/((x^2)+Bx+C)
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Definition
1.) Use the quadratic function on the denominator to generate
Lowest Factor: D
Highest Factor:E
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2.) (-Infinity,D)U(D,E)U(Infinity,E)
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What is the domain of this function?
A/((x^2)+Bx+C)
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Definition
1.) Use the quadratic function on the denominator to generate
Lowest Factor: D
Highest Factor:E
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2.) (-Infinity,D)U(D,E)U(Infinity,E)
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What are the vertical asymptotes of this function?
((x+A)(Bx-B)/(x-C)(x+D))
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Definition
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What is the horizontal asymptote of this function?
-Ax+B/Cx+D
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Definition
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How do you graph this function?
1/(x+A)
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Definition
It looks like an omnitrix symbol
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What is the horizontal asymptote of this function?
(((x^2)+Ax-B)/x-B)
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Definition
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