1.3 Solving Equations Using a Graphing Utility; Solving Linear and Quadratic Equations

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1.3Solving Equations Using a Graphing Utility
Solving Linear and Quadratic Equations
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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.
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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 Zero-Product Property.

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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).

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Solve a linear equation 5x - 4 7.
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Solve by Zero-Product Property
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Zero-Product Property
The solution set is 0, 6.
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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.

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Steps for Approximating Solutions of Equations
Using Intersect

• Graph Y1expression in x on the left hand side
  of equation.
• Graph Y2expression in x on the right hand side
  of equation.
• Use INTERSECT to determine each x-coordinate of
  the points of intersection.

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Linear Equations
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Quadratic Equations

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Methods for Solving Quadratic Equations

• Factoring
• Graphing
• Square Root Method
• Complete the Square Method
• Quadratic Formula

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The Square Root Method
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Solve the following quadratic equation
Using the Square Root Method
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Solve by completing the square.
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Quadratic Formula
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Discriminant of a Quadratic Equation
is called a discriminant
gt0, there are 2 unequal real solutions.
0, there is a repeated real solution.
lt0, there is no real solution.