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Thank you for visiting our site! You landed on this page because you entered a search term similar to this:
solve and graph non liner system of equations, here's the result:
 Understand the
Cartesian coordinate system and the idea of locating ordered
pairs of numbers.
 Know and use the
midpoint and distance formulas to solve real world problems.
 Know how to graph
relations in the coordinate plane.
 Find domain
and range of a relation from a list or ordered pairs, graph or
a table of values.
 Recognize and
evaluate basic features of a graph of a relation.
 Produce graphs
of simple relations using tables.
 Find the x
and yintercepts of the graph of an equation (algebraically and
graphically)
 Determine the
symmetry of the graph of an equation (algebraically and graphically)
 Write the General
Form Equation of a circle in Standard Form and determine the center
and radius of the circle

Basic Features
of a Graph
 domain and
restricted values
 range
 x
and y intercepts
 intervals
where a graph is constant, increasing or decreasing


Linear Equations and Inequalities
 Solve linear
equations algebraically and graphically.
 Deal with fractional
coefficients in equations.
 Solve equations
involving absolute value algebraically.
 Solve a formula
for a given variable.
 Solve word problems
by setting up and solving a linear equation in one variable.
 Solve linear inequalities
in one variable including compound inequalities and inequalities involving
absolute value algebraically.
 Represent (graph or
plot) solution sets of inequalities on the number line.
Quadratic Equations
 Solve quadratic
equations by a variety of methods.
 Use the discriminant
to understand when a quadratic has no, one or two real roots algebraically.
 Solve simple word
problems using quadratic equations
 Construct and
use a quadratic model to solve an application problem

Methods of
Solving Quadratics
 By factoring
and Using Zero Factor Property when possible.
 By extracting
square roots
 By completing
the square
 Using the
Quadratic formula


Polynomials and Polynomial
Expressions
 Perform basic
operations with polynomials (add, subtract, multiply including
FOIL)
 Use formulas for
these special products:
 Factor polynomials
by factoring out the Greatest Common Factor,
by grouping, and by using special products formulas for trinomials
 Factor simple
trinomials of form a x^{2} + b x + c
by guessandcheck or by grouping
 Solve simple equations
using the Zero Factor Property when possible.
 Solve polynomial
inequalities (degree > 1)

The
Special products:
 (a
+ b)^{2}
 (a
 b)^{2}
 (a
+ b)(a  b)


Solving
Nonlinear Inequalities
 Use
critical numbers to determine test intervals for a polynomial
inequality
 Solve
a polynomial inequality algebraically and graphically
 Construct
and use a polynomial inequality to solve an application
problem



Rational Expressions
 Know how to decide the
domain of a rational expressions. (Decide what values are excluded by the
denominator.)
 Simplify and perform
basic operations involving rational expressions (addition, subtraction, multiplication,
division)
 Find a Least Common
Denominator and use it to add or subtract rational expressions.
 Solve equations with
rational expressions. Recognize that some solutions may be extraneous and
check for that.
 Within the context of
sections covered, apply rational expressions to simple situations.
Other Types of
Equations and Inequalities
 Solve equations involving
radicals or rational exponents
 Solve equations involving
rational fractions
 Solve equations involving
absolute values
 Solve higher degree
polynomial equations by factoring
 Solve equations methods
as appropriate.
Equations of the
Line and Linear Inequalities

Representations
of a line:
 Standard
form: A x + B y =
C where A, B, and C are any real numbers.
 Slopeintercept
form: y = m x + b
where m is the slope of a line and b is the yintercept.
 Pointslope
form: y  k = m (x  h)
where (h,k) is any point on the line.


Special Slope
Relationships.
 Horizontal
lines (m = 0)
 Vertical
lines (m is undefined)
 Parallel
lines (m_{1 }= m_{2})
 Perpendicular
lines (m_{1 }m_{2} = 1)


General Function
Concepts
Definition and Notation
 Determine if an
equation or a set of ordered pairs represents a function
 Use function notation
 Evaluate a function
 Find the domain
of a function
 Create and apply
a piecewisedefined function.
 Interpret input
and output of reallife functions
 Solve an application
problem involving reallife functions
Graphs of functions
 Find domain and
range using the graph of a function
 Vertical Line Test
 Describe the increasing
and decreasing behavior of a function
 Classify a function
as even or odd
 Identify six common
graphs
Transformations
of Functions
 Sketch the graph
of a function using common graphs and transformations
 Write the equation
of function using common graphs and transformations
Algebra of Functions
 Find the sum, difference,
product, and quotient of functions
 Find the composition
of two functions and determine the domain and range
 Identify a function
as the composition of two functions
 Solve reallife
problems involving combinations and composition of functions
Inverse Functions
 Determine if a
function has an inverse function (Horizontal Line Test)
 Find the Inverse
of a function
 Graph a function
and its Inverse (Know that the graph of f^{
1} is a reflection of the
graph of f across the line y
= x.)
Polynomial Functions
Polynomial division
 Divide polynomials
using long division
 Divide polynomials
using Synthetic division
 Use the Remainder
Theorem to evaluate a polynomial
 Use the Factor
Theorem to factor a polynomial
Complex numbers (if
covered by your instructor)
 Perform operations
with complex numbers and write the results in standard form
 Solve a quadratic
equation involving complex zeros
Polynomial analysis
Rational Functions
 Find the domain of
a rational function
 Find the vertical
and horizontal asymptotes of the graph of a rational function
 Sketch the graph
of a rational function
 Use a rational function
model to solve an application problem
Exponential Functions
 Sketch the graph
of an exponential function
 Investigate basic
characteristics of an exponential function (domain, range, intercepts, increasing/decreasing
behavior)
 Write formulas of
transformed exponential functions
 Use an exponential
model to solve an application problem (in particular, models involving the
natural exponential function)
 Use the compound
interest formula to solve finance problems
 Construct and use
a model for exponential growth or exponential decay
Logarithmic Functions
 Properties of logarithms
 Solve Logarithmic
and Exponential Equations
 Sketch the graph
of a logarithmic function
 Investigate basic
characteristics of a logarithmic function (domain, xintercept, vertical
asymptote)
 Write formulas of
transformed logarithmic functions
 Use a logarithmic
model to solve an application problem (in particular, models involving the
natural logarithmic function)
Systems in two variables
 Solve a linear
system of equations
 Construct and
use a linear system of equations to solve an application problem
 Solve nonlinear
systems
 Construct and
use a nonlinear system of equations to solve an application problem

Methods of
Solving Systems.
 by substitution
 by elimination
 graphically

