Solving Quadratic EquationsPulling 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: 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 = 0x = -2 x = -3

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

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.

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: x2 + 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 X2 - 4 = 0 X2 - 4x + 4 = 0 X2 + 4x - 4 = 0

Based on the graphs for the equations above, what are thepossibilities for solutions to a quadratic equation?