Solving Quadratic Equations Pulling It All Together Five

Five ways to solve… • • • Factoring Square Root Principle Completing the Square

Solve by Factoring: x 2 + 5 x + 6 = 0 • Get

Solve using the Square Root Principle • Must have “perfect square” variable expression on

Solve by Completing the Square: x 2 + 5 x + 6 = 0

Once the “Square is complete, ” Apply the Square Root Principle • Take the

Solve by Graphing: x 2 + 5 x + 6 = 0 1. Enter

Graph these Quadratics X 2 - 4 = 0 X 2 - 4 x

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Solving Quadratic Equations Pulling It All Together

Five ways to solve… • • • Factoring Square Root Principle Completing the Square Quadratic Formula (not this test, test 3) Graphing

Solve by Factoring: x 2 + 5 x + 6 = 0 • Get all the terms of the polynomial in descending order on one side of the equation and 0 on the other side. x 2 + 5 x + 6 = 0 • Factor the polynomial. (x + 2) (x + 3) = 0 • Apply the zero product rule by setting each factor equal to zero. x + 2 = 0 or x + 3 = 0 • Solve each equation for x. x+2=0 or x + 3 = 0 x = -2 x = -3

Solve using the Square Root Principle • Must have “perfect square” variable expression on one side and constant on the other Examples: x 2 = 16 (x – 4)2 = 9 (2 x – 1)2 = 5

Solve by Completing the Square: x 2 + 5 x + 6 = 0 • Gather the x-terms to one side of the equation and the constant terms to the other side and simplify if possible. x 2 + 5 x = -6 • Divide the coefficient of x by 2, square the result, and add this number to both sides of the equation. x 2 + 5 x = -6 • Factor the polynomial and simplify the constants.

Once the “Square is complete, ” Apply the Square Root Principle • Take the square root of both sides (be sure to include plus/minus in front of the constant term). • • Simplify both sides. Solve for x.

Solve by Graphing: x 2 + 5 x + 6 = 0 1. Enter the polynomial into the “y=“ function of the calculator. 2. Modify the window as needed to accommodate the graph. x = -3 x = -2 3. Locate the x-intercepts of the graph. These are the solutions to the equation.

Graph these Quadratics X 2 - 4 = 0 X 2 - 4 x + 4 = 0 X 2 + 4 x - 4 = 0 Based on the graphs for the equations above, what are the possibilities for solutions to a quadratic equation?