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

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

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

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  1. 1.3Solving Equations Using a Graphing Utility; Solving Linear and Quadratic Equations

  2. 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.

  3. 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. Procedures that Result in Equivalent Equations

  4. 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).

  5. Solve a linear equation 5x - 4 = 7.

  6. Solve by Zero-Product Property

  7. Zero-Product Property The solution set is {0, 6}.

  8. 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.

  9. 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.

  10. Linear Equations

  11. Quadratic Equations

  12. Methods for Solving Quadratic Equations • Factoring • Graphing • Square Root Method • Complete the Square Method • Quadratic Formula

  13. The Square Root Method

  14. Solve the following quadratic equation: Using the Square Root Method

  15. Solve by completing the square.

  16. Quadratic Formula

  17. 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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