Download NCTM Algebra Standards Grades 9-12

E R R O R S , M I S H A P S , A N D M I S C O N C E P T I O N S :
U N D E R S T A N D I N G Q U A D R A T I C F U N C T I O N S
NCTM Algebra Standards: Grades 9-12 Expectations
(from Principles and Standards for School Mathematics © 2000)
Instructional programs from prekindergarten through grade In grades 9–12 all students should –
12 should enable all students to –
Understand patterns, relations, and functions
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Represent and analyze mathematical situation and
structure using algebraic symbols
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Use mathematical models to represent and
understand quantitative relationships
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generalize patterns using explicitly defined and
recursively defined functions;
understand relations and functions and select,
convert flexibly among, and use various
representations for them;
analyze functions of one variable by
investigating rates of change, intercepts, zeros,
asymptotes, and local and global behavior;
understand and perform transformations such
as arithmetically combining, composing, and
inverting commonly used functions, using
technology to perform such operations on
more-complicated symbolic expressions;
understand and compare the properties of
classes of functions, including exponential,
polynomial, rational, logarithmic, and periodic
functions;
interpret representations of functions of two
variables.
understand the meaning of equivalent forms of
expressions, equations, inequalities, and
relations;
write equivalent forms of equations,
inequalities, and systems of equations and solve
them with fluency—mentally or with paper and
pencil in simple cases and using technology in
all cases;
use symbolic algebra to represent and explain
mathematical relationships;
use a variety of symbolic representations,
including recursive and parametric equations,
for functions and relations;
judge the meaning, utility, and reasonableness
of the results of symbol manipulations,
including those carried out by technology.
identify essential quantitative relationships in a
situation and determine the class or classes of
functions that might model the relationships;
E R R O R S , M I S H A P S , A N D M I S C O N C E P T I O N S :
U N D E R S T A N D I N G Q U A D R A T I C F U N C T I O N S
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Analyze change in various contexts
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use symbolic expressions, including iterative
and recursive forms, to represent relationships
arising from various contexts;
draw reasonable conclusions about a situation
being modeled.
approximate and interpret rates of change from
graphical and numerical data.
E R R O R S , M I S H A P S , A N D M I S C O N C E P T I O N S :
U N D E R S T A N D I N G Q U A D R A T I C F U N C T I O N S
MA Frameworks/Common Core
The Complex Number System
N-CN
Use complex numbers in polynomial identities and equations.
7.
Solve quadratic equations with real coefficients that have complex solutions.
Seeing Structure in Expressions
A-SSE
Write expressions in equivalent forms to solve problems.
3.
Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of
the function it defines.
Reasoning with Equations and Inequalities
A-REI
Solve equations and inequalities in one variable.
4.
Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an
equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula
from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing
the square, the quadratic formula, and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives complex solutions and write them as
a ± bi for real numbers a and b.
MA.4.c. Demonstrate an understanding of the equivalence of factoring, completing the square, or
using the quadratic formula to solve quadratic equations.
Interpreting Functions
F-IF
Analyze functions using different representations.
7.
Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases. 
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
8.
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.
Linear, Quadratic, and Exponential Models
F-LE
Construct and compare linear, quadratic, and exponential models and solve problems.
3.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 
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