1. ALGEBRA – LESSON 119 Quadratic Formulas Be ready to grade the homework!

2. 2 Quadratic Formula Any equation that can be put into the form ax 2 + bx + c = 0 is called a quadratic equation. Each of the following is a quadratic equation: x 2 + 9x + 14 = 0 2x 2 - 3x = 8 Note that this one can be rearranged to be 2x 2 - 3x – 8 = 0 3x 2 - 48x = 0 Note that this one can be rewritten to be 3x 2 - 48x + 0 = 0 As long as the coefficent of x 2 is not zero, it can be a quadratic equation.

3. 3 Quadratic Formula Some of these equations can be solved by easy factoring. x 2 + 3x – 10 = 0(x + 5) Once we have factored the equation, we know that as long as EITHER binomial = 0, then the entire equation will equal zero. Therefore, these equations will have 2 possible answers. (x + 5) = 0 (x – 2) = 0 (x – 2) = 0 OR Therefore x = -5 OR x = 2

4. 4 Quadratic Formula Most quadratics cannot be solved with easy factoring. We need to use the quadratic formula to solve those. 2x 2 – 4x – 5 = 0 The Quadratic Formula: We cannot factor this with the methods we’ve learned before. – b  b 2 – 4 a c 2a x = a = b = c = 2 - 4 - 5

5. 5 Quadratic Formula 1) Rewrite the equation in descending order so that it equals zero. 2) Look at the values for a, b and c. Be careful to include any negatives! 3) Plug the values into the Quadratic Formula. 4) Solve – be sure to find one answer using + and one answer using – in front of the radical.

6. Quadratic Formula Solve 7x 2 - 11x = -2 by using the quadratic formula. – b  b 2 – 4 a c 2a x = a = b = c = b 2 = 4ac = 7 -11 2 11  121 – 56 14 x = 121 56 Work the problem twice – once with addition and once with subtraction. 11 + 65 14 x = 11 – 65 14 x =  1.36 .21 7x 2 - 11x + 2 = 0 #1

7. Quadratic Formula Solve 2x 2 + 1 = 7x by using the quadratic formula. – b  b 2 – 4 a c 2a x = a = b = c = b 2 = 4ac = 2 -7 1 7  49 – 8 4 x = 49 8 Work the problem twice – once with addition and once with subtraction. 7 + 41 4 x = 7 – 41 4 x =  3.35 .15 2x 2 - 7x + 1 = 0 #2

8. Quadratic Formula Solve 4x 2 – 7x = -1 by using the quadratic formula. – b  b 2 – 4 a c 2a x = a = b = c = b 2 = 4ac = 4 -7 1 7  49 – 16 8 x = 49 16 Work the problem twice – once with addition and once with subtraction. 7 + 33 8 x = 7 – 33 8 x =  1.59 .16 4x 2 - 7x + 1 = 0 #3

9. #4 Quadratic Formula Solve 2x 2 – 1 = 5x by using the quadratic formula. – b  b 2 – 4 a c 2a x = a = b = c = b 2 = 4ac = 2 -5 5  25 + 8 4 x = 25 -8 Work the problem twice – once with addition and once with subtraction. 5 + 33 4 x = 5 – 33 4 x =  2.69  -.19 2x 2 - 5x - 1 = 0

10. Homework: Worksheet