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Review of Quadratic Formula
The quadratic formula is derived from completing the square on the general equation: 2 ax bx c 0 You MUST memorize the formula: 2 4 2 b b ac x a
Process:
- Write the equation in standard form: 2 ax bx c 0
- Identify (^) a b , , and c.
- Substitute numbers into formula.
- Carefully do the arithmetic under the square root sign.
- If possible, simplify the radical.
- If possible, reduce the fraction.
2 3 x 2 x 4 0 2. 2 8 x 5( x 1)
- 4 ( x x 1) 5 0
Quadratic Types of Equations
Review of Factoring: In previous math classes, you have learned to solve quadratic equations by the factoring method. 2 4 x 8 x 3 0 2 5 x 19 x 4 0 Quadratic Types of Equations: We have equations that look like a quadratic, but have different exponents. Some examples of these equations are: 4 2 4 x 8 x 3 0 2 1 5 x^3 19 x^3 4 0 6 x ^2 7 x ^1 3 0 Solve by factoring:
4 2 4 x 8 x 3 0 2. 2 1 5 x^3 19 x^3 4 0
Equations with Fractional Exponents
Review of Exponents: Remember that a fractional exponent can be written in radical form.
3 23 x^2 x
2 52 x^5 x If you encounter an equation that has a variable raised to a fractional exponent, you solve it by raising both sides to the appropriate power.
3 23 x^2 x
2 52 x^5 x Solve:
3 2 2
x 6 x 7 27 6.
2 x 2 3 9
1 1 x 2 2 11 x 2 4 18
