| (C) solve systems of two linear equations with two
variables for mathematical and real-world problems.
(6) Quadratic functions and equations. The student
applies the mathematical process standards when using properties of
quadratic functions to write and represent in multiple ways, with
and without technology, quadratic equations. The student is expected
to:
(A) determine the domain and range of quadratic functions
and represent the domain and range using inequalities;
(B) write equations of quadratic functions given the
vertex and another point on the graph, write the equation in vertex
form (f(x) = a(x - h)2 + k), and rewrite the equation from vertex
form to standard form (f(x) = ax2 + bx + c); and
(C) write quadratic functions when given real solutions
and graphs of their related equations.
(7) Quadratic functions and equations. The student
applies the mathematical process standards when using graphs of quadratic
functions and their related transformations to represent in multiple
ways and determine, with and without technology, the solutions to
equations. The student is expected to:
(A) graph quadratic functions on the coordinate plane
and use the graph to identify key attributes, if possible, including x- intercept, y- intercept,
zeros, maximum value, minimum values, vertex, and the equation of
the axis of symmetry;
(B) describe the relationship between the linear factors
of quadratic expressions and the zeros of their associated quadratic
functions; and
(C) determine the effects on the graph of the parent
function f(x) = x2 when f(x) is replaced by af(x),
f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
(8) Quadratic functions and equations. The student
applies the mathematical process standards to solve, with and without
technology, quadratic equations and evaluate the reasonableness of
their solutions. The student formulates statistical relationships
and evaluates their reasonableness based on real-world data. The student
is expected to:
(A) solve quadratic equations having real solutions
by factoring, taking square roots, completing the square, and applying
the quadratic formula; and
(B) write, using technology, quadratic functions that
provide a reasonable fit to data to estimate solutions and make predictions
for real-world problems.
(9) Exponential functions and equations. The student
applies the mathematical process standards when using properties of
exponential functions and their related transformations to write,
graph, and represent in multiple ways exponential equations and evaluate,
with and without technology, the reasonableness of their solutions.
The student formulates statistical relationships and evaluates their
reasonableness based on real-world data. The student is expected to:
(A) determine the domain and range of exponential functions
of the form f(x) = abx and
represent the domain and range using inequalities;
(B) interpret the meaning of the values of a and b in
exponential functions of the form f(x) =
abx in real-world problems;
(C) write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems
arising from mathematical and real-world situations, including growth
and decay;
(D) graph exponential functions that model growth and
decay and identify key features, including y- intercept
and asymptote, in mathematical and real-world problems; and
(E) write, using technology, exponential functions
that provide a reasonable fit to data and make predictions for real-world
problems.
(10) Number and algebraic methods. The student applies
the mathematical process standards and algebraic methods to rewrite
in equivalent forms and perform operations on polynomial expressions.
The student is expected to:
(A) add and subtract polynomials of degree one and
degree two;
(B) multiply polynomials of degree one and degree two;
(C) determine the quotient of a polynomial of degree
one and polynomial of degree two when divided by a polynomial of degree
one and polynomial of degree two when the degree of the divisor does
not exceed the degree of the dividend;
(D) rewrite polynomial expressions of degree one and
degree two in equivalent forms using the distributive property;
(E) factor, if possible, trinomials with real factors
in the form ax2 + bx + c, including perfect square trinomials
of degree two; and
(F) decide if a binomial can be written as the difference
of two squares and, if possible, use the structure of a difference
of two squares to rewrite the binomial.
(11) Number and algebraic methods. The student applies
the mathematical process standards and algebraic methods to rewrite
algebraic expressions into equivalent forms. The student is expected
to:
(A) simplify numerical radical expressions involving
square roots; and
(B) simplify numeric and algebraic expressions using
the laws of exponents, including integral and rational exponents.
(12) Number and algebraic methods. The student applies
the mathematical process standards and algebraic methods to write,
solve, analyze, and evaluate equations, relations, and functions.
The student is expected to:
(A) decide whether relations represented verbally,
tabularly, graphically, and symbolically define a function;
(B) evaluate functions, expressed in function notation,
given one or more elements in their domains;
(C) identify terms of arithmetic and geometric sequences
when the sequences are given in function form using recursive processes;
(D) write a formula for the nth term of arithmetic and geometric
sequences, given the value of several of their terms; and
(E) solve mathematic and scientific formulas, and other
literal equations, for a specified variable.
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