Quadratic Solutions The number of real solutions is at most two. No solutionsOne solutionTwo solutions The solutions are located on the x axis, or the.

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Presentation transcript:

Quadratic Solutions The number of real solutions is at most two. No solutionsOne solutionTwo solutions The solutions are located on the x axis, or the x value when y=0. The solutions are sometimes called zeroes or roots

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:

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

Examples: 11.6 – Solving Quadratic Equations by Factoring

Solving Quadratic Equations: 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? 11.7 – Quadratic Equations and Problem Solving

The square of a number minus twice the number is 63. Find 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? 11.7 – Quadratic Equations and Problem Solving

Find two consecutive odd numbers whose product is 23 more than their sum? 11.7 – Quadratic Equations and Problem Solving