'Imaginary solutions' presentation slideshows

5.1

5.1. A quadratic function f is a function of the form f(x) = ax 2 + bx + c where a, b and c are real numbers and a not equal to zero. The graph of the quadratic function is called a parabola. It is a "U" shaped curve that may open up or down depending on the sign of coefficient a.

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r eview: completing the square

In this lesson, you will learn to solve any equation of the form (with real coefficients), including equations with imaginary solutions, by completing the square. r eview: completing the square. r eview: completing the square. Solve . . r eview: completing the square. Solve . .

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Solving Quadratics by Completing the Square & Quadratic Formula

Solving Quadratics by Completing the Square & Quadratic Formula. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: October 24, 2007. X 2 + 6x + 9. x. 1. 1. 1. 1. 1. 1. x. x + 3. Now, complete the square. 1. + 9. 1. 1. x + 3. Jeff Bivin -- LZHS.

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Warm-up

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Warm Up

Warm Up. Solve the following equations. 4.4 Complex Numbers (PART 1). The problem is square roots . Every positive number has 2 square roots. So what happens when I want to take the square root of a negative number?. Problem with Square Roots.

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Do Now

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Algebra 2

Algebra 2. Section 4.7 Complete the Square Section 4.8 Quadratic Formula and the Discriminant. 4.7 Complete the Square . Standard Form ax 2 + bx + c Intercept Form m(x - p)(x - q) Vertex Form m(x -d) 2 + b. Example 1: 4.7.

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Chapter 5.9

Chapter 5.9. Complex Numbers. Objectives. To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary solutions. To add, subtract, and multiply complex numbers. Why is this important?

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Imaginary Number:

Imaginary Number:. POWERS of i: Is there a pattern?. Pattern repeats every 4 th power : Divide power by 4 and use remainder. Ex:. I ONE, I ONE! LOSERS IN THE MIDDLE. LOSERS=NEGATIVE. Example 1: Simplifying Powers of i. [B]. [C]. [A]. [D]. [E]. [E]. [B]. [C]. [E]. [D]. [F].

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5.6 Quadratic Formula & Discriminant

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2.6 Solving Quadratic Equations with Complex Roots

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Roots and Zeros

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