1. 1.4 Solving Equations Using a Graphing Utility

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. 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.

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. 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.

18. Equations Containing Radicals

22. Thus 85 is NOT a solution.
The solution set is {5}.

23. Equations Involving Absolute Value

24. The solution set is {7,-6}.