1. Bellwork A softball is thrown upward with an initial velocity of 32 feet per second from 5 feet above the ground. The ball’s height in feet above the ground is modeled by h(t) = -16t² +32t + 5, where t is the time in seconds after the ball is released. 1. Sketch the graph of the quadratic function. Be sure to label the x and y axis. 2. Find the x-intercepts. Round to the nearest hundredth. 3. Find the maximum height of the ball. 4. How long does it take the ball to reach the max height?

2. LESSON 5.6 Quadratic Equations and Complex Numbers

3. Special Notes = =i i² = = -1 = = -i = -1 -1 = 1

4. Operations with Imaginary Numbers Examples: 1. (-3 + 5i) + (7-6i) 2. 2i( 5 +5i) 3. (2 + i)(-5 -3i) 4. (-2i)²

5. Practice Simplify. #1) #2) (-4 + 2i)(3 – i) #3) (6-4i) – (2 + 8i) #4) 2i( 5 +5i)

6. Lesson 5.6 The Conjugate of a Complex Number. A conjugate of a complex number a + bi is a – bi. The conjugate of a – bi is a + bi. EXAMPLE: What is the conjugate of 2 +4i? What is the conjugate of 7-3i? To simplify a quotient with an imaginary number in the denominator, multiply by a fraction equal to, using the conjugate of the denominator. This process is called rationalizing the denominator. EXAMPLE:

7. 1. 2. Practice:

8. WORKSHEET 5.6 HOMEWORK