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6.6 Solving Quadratic EquationsPowerPoint Presentation

6.6 Solving Quadratic Equations

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6.6 Solving Quadratic Equations. Objectives: Multiply binominals using the FOIL method. Factor Trinomials. Solve quadratic equations by factoring. Solve quadratic equations using the quadratic formula. Page 317.

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### 6.6 Solving Quadratic Equations

### Homework Assignment on the Internet quadratic equation when put in the form general form.

Objectives:

Multiply binominals using the FOIL method.

Factor Trinomials.

Solve quadratic equations by factoring.

Solve quadratic equations using the quadratic formula.

Page 317

- A binomial expression has just two terms (usually an x term and a constant). There is no equal sign. Its general form is ax + b, where a and b are real numbers and a ≠ 0.
- One way to multiply two binomials is to use the FOIL method. FOIL stands for the pairs of terms that are multiplied: First, Outside, Inside, Last.
- This method works best when the two binomials are in standard form (by descending exponent, ending with the constant term).
- The resulting expression usually has four terms before it is simplified. Quite often, the two middle (from the Outside and Inside) terms can be combined.

For example: and a constant). There is no equal sign. Its general form is

- The and a constant). There is no equal sign. Its general form is opposite of multiplying two binomials is to factor or break down a polynomial (many termed) expression.
- Several methods for factoring are given in the text. Be persistent in factoring! It is normal to try several pairs of factors, looking for the right ones.
- The more you work with factoring, the easier it will be to find the correct factors.
- Also, if you check your work by using the FOIL method, it is virtually impossible to get a factoring problem wrong.
- Remember! When factoring, always take out any factor that is common to all the terms first.

- A quadratic equation involves a single variable with exponents no higher than 2.
- Its general form is where a, b, and c are real numbers and .
- For a quadratic equation it is possible to have two unique solutions, two repeated solutions (the same number twice), or no real solutions.
- The solutions may be rational or irrational numbers.

- To solve a quadratic equation, if it is factorable: exponents no higher than 2.
- 1. Make sure the equation is in the general form.
- 2. Factor the equation.
- 3. Set each factor to zero.
- 4. Solve each simple linear equation.

To solve a quadratic equation if you can’t factor the equation:

- Make sure the equation is in the general form.
- Identify a, b, and c.
- Substitute a, b, and c into the quadratic formula:
- Simplify.

- The beauty of the quadratic formula is that it works on any quadratic equation when put in the form general form.
- If you are having trouble factoring a problem, the quadratic formula might be quicker.
- Always be sure and check your solution in the original quadratic equation.

<> quadratic equation when put in the form general form.

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Find the product: quadratic equation when put in the form general form.

Factor quadratic equation when put in the form general form.x2 - 7x + 12.

1. Pairs of numbers which make 12 when multiplied: (1, 12), (2, 6), and (3, 4).

- 1 + 12≠7. 2 + 6≠7. 3 + 4 = 7. Thus, d = 3 and e = 4.
- (x - 3)(x - 4)
- Check: (x - 3)(x - 4) = x2 -4x - 3x + 12 = x2 - 7x + 12
- Thus, x2 - 7x + 12 = (x - 3)(x - 4).

Factor 2 quadratic equation when put in the form general form.x3 +4x2 + 2x.

First, remove common factors: 2x3 +4x2 +2x = 2x(x2 + 2x + 1)

- Pairs of numbers which make 1 when multiplied: (1, 1).
- 1 + 1 = 2. Thus, d = 1 and e = 1.
- 2x(x + 1)(x + 1) (don't forget the common factor!)
- Check: 2x(x + 1)(x + 1) = 2x(x2 +2x + 1) = 2x3 +4x2 + 2x
- Thus, 2x3 +4x2 +2x = 2x(x + 1)(x + 1) = 2x(x + 1)2.x2 + 2x + 1 is a perfect square trinomial.

The Box Method for Factoring a Polynomial quadratic equation when put in the form general form.

The Box Method for Factoring a Polynomial quadratic equation when put in the form general form.

Factor the trinomial: quadratic equation when put in the form general form.

Use the Quadratic Formula to solve quadratic equation when put in the form general form.

Solve for x: quadratic equation when put in the form general form.

Solve for x: quadratic equation when put in the form general form.

Solve using the quadratic formula: quadratic equation when put in the form general form.

Section 6.6 (Read Solving Quadratic Equation)

Pp 329-330: 2-78even.

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