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Published byNicholas Phelps Modified over 5 years ago
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1.4 Solving Equations Using a Graphing Utility
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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 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 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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Quadratic Formula
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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.
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Equations Containing Radicals
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Thus 85 is NOT a solution. The solution set is {5}.
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Equations Involving Absolute Value
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The solution set is {7,-6}.
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