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5.5 The Quadratic Formula

As you come in collect your Warm-Ups to be turned in. Place them on the seat of the desk. (you should have 10, be sure to write absent for the ones you were absent for; if you do not they will be counted as missing)

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5.5 The Quadratic Formula

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  1. As you come in collect your Warm-Ups to be turned in. Place them on the seat of the desk. (you should have 10, be sure to write absent for the ones you were absent for; if you do not they will be counted as missing) Also grab a Project Rubric from the desk and you and your partner need to fill it out.

  2. 5.5 The Quadratic Formula

  3. Quadratic Formula Quadratic Formula Song x equals negative b plus or minus, square root b squared minus four, a, c all over two, a

  4. Solving Using the Quadratic Formula Example 1: x2 + 7x + 9 = 0 a = 1 b = 7 c = 9

  5. Solving Using the Quadratic Formula Example 2: 5x2 + 16x – 6 = 3 a = 5 b = 16 c = -9

  6. 5.6 Quadratic Equations and Complex Numbers

  7. What the Discriminant Tells Us… • If it is positive then the formula will give 2 different answers • If it is equal to zero the formula will give only 1 answer • This answer is called a double root • If it is negative then the radical will be undefined for real numbers thus there will be no real zeros.

  8. The Discriminant • When using the Quadratic Formula you will find that the value of b2 - 4ac is either positive, negative, or 0. • b2 - 4ac called the Discriminantof the quadratic equation.

  9. Finding the Discriminant Find the Discriminant and determine the numbers of real solutions. Example 1: x2+ 5x + 8 = 0 How many real solutions does this quadratic have? b/c discriminant is negative there are no real solutions

  10. Finding the Discriminant Find the Discriminant and determine the numbers of real solutions. Example 2: x2 – 7x = -10 How many real solutions does this quadratic have? b/c discriminant is positive there are 2 real solutions

  11. Imaginary Numbers • What if the discriminant is negative? • When we put it into the Quadratic Formula can we take the square root of a negative number? • We call these imaginary numbers • An imaginary number is any number that be re written as:

  12. Imaginary Numbers Example 1: Example 2:

  13. Complex Numbers • A complex number is any number that can be written as a + bi, where a and b are real numbers; a is called the real part and b is called the imaginary part.

  14. Operations with Complex Numbers • Find each sum or difference: • (-3 + 5i) + (7 – 6i) = • (-3 – 8i) – (-2 – 9i) =

  15. Operations with Complex Numbers • Multiply: (2 + i)(-5 – 3i) =

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