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Published byScarlett Hamilton Modified over 4 years ago

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**As you come in collect your Warm-Ups to be turned in**

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.

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5.5 The Quadratic Formula

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

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**Solving Using the Quadratic Formula**

Example 1: x2 + 7x + 9 = 0 a = 1 b = 7 c = 9

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**Solving Using the Quadratic Formula**

Example 2: 5x2 + 16x – 6 = 3 a = 5 b = 16 c = -9

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**5.6 Quadratic Equations and Complex Numbers**

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**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.

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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 Discriminant of the quadratic equation.

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**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

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**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

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**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:

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Imaginary Numbers Example 1: Example 2:

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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.

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**Operations with Complex Numbers**

Find each sum or difference: (-3 + 5i) + (7 – 6i) = (-3 – 8i) – (-2 – 9i) =

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**Operations with Complex Numbers**

Multiply: (2 + i)(-5 – 3i) =

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