Factoring to Solve Quadratic Equations. 11.6 – Solving Quadratic Equations by Factoring A quadratic equation is written in the Standard Form, where a,

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Presentation transcript:

Factoring to Solve Quadratic Equations

11.6 – Solving Quadratic Equations by Factoring A quadratic equation is written in the Standard Form, where a, b, and c are real numbers and. Examples: (standard form)

Zero Factor Property: If a and b are real numbers and if, Examples: then or – Solving Quadratic Equations by Factoring

Zero Factor Property: If a and b are real numbers and if, Examples: then or – Solving Quadratic Equations by Factoring

Solving Quadratic Equations: 1) Write the equation in standard form. 4) Solve each equation. 2) Factor the equation completely. 3) Set each factor equal to 0. 5)Check the solutions (in original equation). ***roots, solutions, zeros*** 11.6 – Solving Quadratic Equations by Factoring

If the Zero Factor Property is not used, then the solutions will be incorrect 11.6 – Solving Quadratic Equations by Factoring

A cliff diver is 64 feet above the surface of the water. The formula for calculating the height (h) of the diver after t seconds is: How long does it take for the diver to hit the surface of the water? seconds 11.7 – Quadratic Equations and Problem Solving

The square of a number minus twice the number is 63. Find the number. x is the number – Quadratic Equations and Problem Solving

The length of a rectangular garden is 5 feet more than its width. The area of the garden is 176 square feet. What are the length and the width of the garden? The width is w.The length is w+5. feet 11.7 – Quadratic Equations and Problem Solving