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Ch3/4 Lesson 2 Solving Quadratic Functions by Factoring

Learn how to factor quadratic equations and solve for 'x', covering difference of squares, solving trinomials, and applying quadratic functions with real-world examples.

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Ch3/4 Lesson 2 Solving Quadratic Functions by Factoring

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  1. Ch3/4 Lesson 2Solving Quadratic Functions by Factoring

  2. I) Review: Factoring a Difference of Squares • Difference  Subtraction • Difference of Squares  Subtraction of two perfect squares • When you multiply a binomial with its conjugate, the product will be a “difference of squares”

  3. Ex: Factor completely

  4. I) What does Solving Mean? • What Does “Solving” Mean? Finding a value for “x” (Variable) so that both sides of an equation will be equal Ex: Solve for “x” Both sides will be equal • When you’re “solving” there will always be an equal sign in the equation.

  5. ii) Solving Trinomials by Factoring When you have the product of two brackets equal to zero, you can solve this equation easily: Rule: zero times anything is always equal to zero Make each bracket equal to zero Solve for “x” from each bracket You get two answers, one from each bracket Check:

  6. When solving trinomials, factor the equation to two binomials • Make each binomial equal to zero • Solve for “x” from each bracket Ex: Solve for “x” Factor Make each bracket equal to zero Solve for “x” from each bracket

  7. Practice: Solve for the Roots

  8. More Practice: Solve for the Roots

  9. Even More Practice: Solve

  10. Applications of Quadratic Functions: • Product – means multiply • Consecutive – the terms increase by one • Area of a rectangle – means you multiply the length and width • Two sticks have a length of 20, if one of them have a length of “x”, the other will have a length of • The difference of two numbers is 6 • Sum of their squares – square each number and then add them

  11. Example 4: The difference of two numbers is 4. The sum of their squares is 136. Find the numbers: Let “x” be the first number Let “x + 4” be the Second number The you 2 possible answers for “x” If the first number is –10, the second number is –6 If the first number is 6, the second number is 10

  12. Example 5:The width of a rectangle is 11 cm. less than 3 times the length. If the area is 42 square cm. find the dimensions of the rectangle. Let the length of the rectangle be x and y be the width. That means the length is 6 cm. And therefore, the with is The dimensions are 6 cm × 7cm.

  13. A 32m tall tree is broken during a severe storm. The distance from the base of the tree to the tip where it touches the ground is 16m. At what height did the tree break? The tree broke at a height of 12m

  14. HW: Assignment 4.1

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