1.4 Solving Equations Using a Graphing Utility

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 Zero-Product 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 x-coordinate of the points of intersection.

Linear Equations

Quadratic Equations

Methods for Solving Quadratic Equations 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

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.

Equations Containing Radicals

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

Equations Involving Absolute Value

The solution set is {7,-6}.