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Solving Quadratic Equations Pulling It All Together

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.

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Solving Quadratic Equations Pulling It All Together

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  1. Solving Quadratic EquationsPulling It All Together

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

  3. Solve by Factoring: x2 + 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. x2 + 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

  4. Solve using the Square Root Principle • Must have “perfect square” variable expression on one side and constant on the other Examples: x2 = 16 (x – 4)2 = 9 (2x – 1)2 = 5

  5. Solve by Completing the Square: x2 + 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. x2 + 5x = -6 • Divide the coefficient of x by 2, square the result, and add this number to both sides of the equation. x2 + 5x = -6 • Factor the polynomial and simplify the constants.

  6. 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.

  7. Solve by Graphing: x2 + 5x + 6 = 0 • Enter the polynomial into the “y=“ function of the calculator. • Modify the window as needed to accommodate the graph. • Locate the x-intercepts of the graph. These are the solutions to the equation. x = -3 x = -2

  8. Graph these Quadratics X2 - 4 = 0 X2 - 4x + 4 = 0 X2 + 4x - 4 = 0 Based on the graphs for the equations above, what are the possibilities for solutions to a quadratic equation?

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