Transcript 1.3 Solving Equations Using a Graphing Utility

1.3
Solving Equations Using a Graphing
Utility;
Solving Linear and Quadratic
Equations
An equation in one variable is a statement
in which two expressions, at least one
containing the variable, are equal.
To solve an equation means to find all those
values of the variable that result in a
true statement.
Procedures that Result in Equivalent
Equations
• Interchange the two
sides of the equation.
• Simplify each
side.(Combine like
terms, eliminate
parentheses . . .)
• Add or subtract the
same expression on
both sides .
• Multiply both sides of
the equation by the
same nonzero
expression.
• If one side is zero and
the other can be
factored use the ZeroProduct Property.
Steps for Solving Equations
Algebraically
• List any restrictions on the domain of the variable.
• Simplify the equation by replacing the original
by a succession of equivalent equations using the
procedures listed earlier.
• If the result is a product of factors equal to 0, use
the Zero-Product Property.
• Check your solution(s).
Solve a linear equation 5x - 4 = 7.
Solve by Zero-Product Property
Zero-Product
Property
The solution set is {0, 6}.
Steps for Approximating Solutions of Equations
Using Zero (or Root)
• Write the equation in the form
{expression in x } = 0
• Graph Y1= {expression in x }.
• Use ZERO (or ROOT) to determine each
x-intercept of the graph.
Steps for Approximating Solutions of Equations
Using Intersect
• Graph Y1={expression in x on the left hand
side of equation}.
• Graph Y2={expression in x on the right
hand side of equation}.
• Use INTERSECT to determine each xcoordinate of the points of intersection.
Linear Equations
Quadratic Equations
Methods for Solving Quadratic
Equations
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Factoring
Graphing
Square Root Method
Complete the Square Method
Quadratic Formula
The Square Root Method
Solve the following quadratic equation:
Using the Square Root Method
Solve by completing the square.
Quadratic Formula
Discriminant of a Quadratic
Equation
is called a discriminant
>0, there are 2 unequal real solutions.
=0, there is a repeated real solution.
<0, there is no real solution.