MATHS Targeted Standards (F) Concept: Function (IF) Domain: Interpreting Functions Cluster: Analyze functions using different representations
MATHS.FIF.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, y = (1.2)^{t/10}, and classify them as representing exponential growth or decay.
Student Learning Targets:
Knowledge Targets
I can recall the order of operations.
I can understand and identify a power and its parts (base and exponent).
I can recognize the properties of exponents (i.e. product of powers, power of a power, power of a product).
I can recognize a zero or negative exponent.
I can identify a radical.
I can identify if a radical expression is in simplest form.
I can recognize the properties of radicals, i.e., product, quotient, and sum of radicals.
I can identify perfect squares.
I can define a logarithm.
I can recall properties of logarithms and exponents.
I can recognize common logarithms and natural logarithms.
I can identify an asymptote.
I can recall the change of base formula.
Reasoning Targets
I can analyze an algebraic expression.
I can decide what to do next based on my knowledge of the order of operations.
I can distinguish the difference of when to use each property of radicals.
I can evaluate the properties of radicals.
I can apply the distributive property.
I can analyze what type of factoring technique that should be used for a given expression. (i.e. factor trinomials, factor difference of squares, factor sum and difference of cubes, factor by grouping, factor out the greatest common factor)
I can combine like terms in an expression or equation.
I can convert from a logarithm to exponential expressions.
I can identify an asymptote.
I can expand and condense logarithms.
I can evaluate logarithms and exponential expressions.
I can distinguish between a natural log and common log.
Skills (Performance) Targets
I can simplify an algebraic expression.
I can apply factor using perfect square.
I can do prime factorization.
I can rationalize a denominator.
I can simplify a polynomial expression.
I can multiply polynomials.
I can justify the steps taken in manipulating an expression.
I can complete all necessary steps in order to simplify the expression.
I can distribute and factor an expression.
I can solve for (isolate) a specific variable.
I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.).
I can check the solution.
I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
I can solve for (isolate) a specific variable.
I can write a linear system.
I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
I can check the solution.
I can solve a quadratic.
I can multiply and factor polynomials.
I can solve a linear inequality.
I can graph a linear inequality.
I can solve a system of linear inequalities.
I can graph a system of linear inequalities.
I can check the solution of the system.
I can solve a linear system (substitution, linear combination, graphically).
I can write a linear system.
I can identify the number of solutions of a linear system.
I can identify the most efficient method to solve a system.
I can check the solution of the system.
I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
I can graph logarithmic and exponential functions.
I can solve logarithmic and exponential equations.
I can apply the change of base formula to evaluate a logarithmic expression.
I can graph and determine the equation of an asymptote.
I can write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function.
I can explain different properties of a function that are revealed by writing a function in equivalent forms.
I can use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a realworld situation.
I can use the properties of exponents to interpret exponential functions as growth or decay.
Product Targets
I can
I can
Proficiency Scale
Score
Description
Sample Activity
4.0
In addition to achieving level 3.0 content, the student makes indepth inferences and applications that go beyond what was taught

3.5
In addition to Score 3.0 performance, the student demonstrates indepth inferences and applications regarding the more complex content with partial success.
3.0
The student can:
Write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function
Explain different properties of a function that are revealed by writing a function in equivalent forms
Use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a realworld situation
Use the properties of exponents to interpret exponential functions as growth or decay
The student exhibits no major errors or omissions.
Given f(x)=x25x6:
Rewrite the function in factored form to find the zeros.
Find the x value of the maximum or minimum and state if a maximum or minimum occurs at that x value.
2.5
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0
There are no major errors or omissions regarding the simpler details and processes as the student:
recognizes and recalls specific terminology, such as
exponential growth
exponential decay
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.

0.5
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
Alg II Equivalent Quadratic Expressions Proficiency Scale
Score
Description
Sample Activity
4.0
(advanced)
In addition to Score 3.0, the student demonstrates indepth inferences and applications regarding more complex material that go beyond end of instruction expectations.
Write the equation of the following graph in the three forms. If you cannot write the function in one of the forms, explain why.
3.5
In addition to Score 3.0 performance, the student demonstrates indepth inferences and applications regarding the more complex content with partial success.
3.0
(proficient)
The student can:
explain the different properties of a function that are revealed by writing a function in equivalent forms.
write a function in equivalent forms (factored vs. general form) to show different properties of the function.
The student exhibits no major errors or omissions.
Rewrite the following equation of the parabola in vertex form. Identify the minimum/maximum value.
f(x)=2x^{2}+16x+10
Rewrite the following equation of the parabola in standard form and find the vertex.f(x)=2(2x1)(x+9)
Explain the advantages of each form of a quadratic function.
2.5
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0
(progressing)
There are no major errors or omissions regarding the simpler details and processes as the student can:
identify the different forms of functions (eg. Factored vs. general form) that show different properties of the function.
recognize and recall basic terminology, such as:
factor
intercept
vertex
complete the square
standard form
parabola
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Label each of the following functions with the quadratic form it represents.
f(x)=2x^{2}+5x+9
q(x)=3(2x+5)(x2)
3. g(x)=4(x3)^{2}+6
1.5
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0
(beginning)
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).
0.5
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0
Even with help, the student demonstrates no understanding or skill.