Chapter: 2
Highlight
One
Topic: Polynomial and Rational Functions
Date Section
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Learning Target
Mastered
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2.1
I can analyze graphs of quadratic functions.
Mastered
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2.1
I can graph any quadratic function (plotting five exact points on my
graph). f  x   ax2  bx  c
I can use completing the square to write quadratic functions in standard
form. I can take an equation written in standard form and graph the
Mastered
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2.1
Mastered
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2.1
I can find the vertex, axis of symmetry, x and y intercepts, domain,
range, and max/min value for any quadratic function.
2.1
I can write the equation of a parabola given the vertex and a point.
2.1
I can use quadratic functions to model and solve real-life problems.
Mastered
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Mastered
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Mastered
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function. f  x   a  x  h   k
2
I can use the Leading Coefficient Test (largest exponent and leading
coefficient) to determine the end behavior of graphs of polynomial
functions. I have the notation for end behavior memorized, and I know
2.2
how to fill in the blanks.
Mastered
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2.2
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2.2
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2.2
Mastered
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2.3
Mastered
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2.3
Mastered
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2.3
Mastered
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2.4
Mastered
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2.4
Mastered
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2.4
Mastered
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2.4
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2.4
f  x   ___ as x  ___
f  x   ___ as x  ___
I can use multiple techniques to find the zeros of polynomial functions:
factoring, quadratic formula, factoring by grouping, etc.
I can find and use end behavior and the zeros of polynomial functions
to sketch a graph. I know that if the multiplicity of a zero is even, then
the graph bounces off the x-axis. I know that if the multiplicity of a zero
is odd, then the graph passes/crosses through the x-axis.
I can use the Intermediate Value Theorem to help locate zeros of
polynomial functions.
I can use long division to divide polynomials by other polynomials. I
remember to use zero place holders when necessary.
I can use synthetic division to divide polynomials by binomials of the
form (x – k). I remember to use zero place holders when necessary.
I can use the Remainder Theorem and Factor Theorem. I know that if I
get a zero as a remainder for long or synthetic division, then the value I
divided by is a factor and this helps me to find the zeros of polynomials.
I can use the imaginary unit i to write complex numbers in standard
form. a  bi
I know how to simplify complex numbers when they include imaginaries
with an exponent. For example, 8i 2  8 .
I can add, subtract, multiply, and simplify complex numbers.
I can use complex conjugates to write the quotient of two complex
numbers in standard form.
I can find complex solutions of quadratic equations. I know that if I use
the quadratic formula and get a negative under the square root, then I
will have complex solutions (imaginary zeros).
Highlight
One
Date Section
Taught of Book
Mastered
Need Practice/Help
2.5
Mastered
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2.5
Mastered
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2.5
Learning Target
I can use the Fundamental Theorem of Algebra to determine the
number of zeros of polynomial functions (including real, imaginary, and
repeated zeros).
I can write a list of the possible rational zeros.
p
q
 p
 and synthetic division
q
I can use my list of possible rational roots 
to find the rational zeros of polynomial functions.
I can find conjugate pairs of complex zeros. I know imaginary zeros
always come in pairs. Given some real and imaginary zeros, I can write
a polynomial function. Given a polynomial and one complex zero, I can
find all of the zeros of the polynomial. (see pg 173-174 ex. 6 and 7)
Mastered
Need Practice/Help
2.5
Mastered
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2.5
I can find zeros of polynomials by factoring.
Mastered
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2.5
I can use Descartes’s Rule of Signs and the Upper and Lower Bound
Rules to find the number of possible positive, negative, and imaginary
zeros of polynomials.
Mastered
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2.6
I can find the domain of rational functions.
Mastered
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2.6
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2.6
Mastered
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2.6
I can find the x and y intercepts of a rational function.
Mastered
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2.6
I can sketch graphs of rational functions. I know how to choose
appropriate values for my x/y chart when graphing.
2.6
I can sketch graphs of rational functions that have slant asymptotes.
2.6
I can use rational functions to model and solve real-life problems.
Mastered
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Mastered
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Mastered
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2.7
Mastered
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2.7
Mastered
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2.7
I can find the horizontal asymptotes of graphs of rational functions. I
know the rules, and I have them memorized. I know that when there is
a slant asymptote I must use long division to find its equation.
I know I must set the denominator equation to zero to find the vertical
asymptotes of graphs of rational functions. I know the one exception to
this is if a factor in the denominator cancels with a factor in the
numerator – this means that it is a hole in the graph at that x value.
I can solve polynomial inequalities by finding critical numbers (zeros),
determining test intervals, and testing points within the intervals.
I can solve rational inequalities by finding critical numbers (zeros and
vertical asymptotes), determining test intervals, and testing points
within the intervals.
I can use inequalities to model and solve real-life problems.