Solving Quadratic Equations Pulling It All Together.

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Presentation transcript:

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 + 5x + 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 + 5x + 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 (2x – 1) 2 = 5

Solve by Completing the Square: x 2 + 5x + 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 + 5x = -6 Divide the coefficient of x by 2, square the result, and add this number to both sides of the equation. x 2 + 5x = -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 + 5x + 6 = 0 x = -3 x = -2 1.Enter the polynomial into the “y=“ function of the calculator. 2.Modify the window as needed to accommodate the graph. 3.Locate the x-intercepts of the graph. These are the solutions to the equation.

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