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This lesson dives into the world of quadratic equations and inequalities, equipping students with tools to represent real-world relationships using these mathematical forms. Learn how to solve quadratic equations using various methods, including the quadratic formula, factoring, and completing the square. Understand the significance of the discriminant in determining the nature of roots—real or complex. The lesson emphasizes using technology for solutions and focuses on substituting coefficients into the quadratic formula. Engage with practice problems and deepen your understanding of quadratic relationships.
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5.6 Quadratic Formula 9.2.4.1 Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.
Guiding Question: How can I find the solutions of a quadratic without graphing, factoring or completing the square? • Lesson Objective: I will be able to take the coefficients of a quadratic function, substitute them into the quadratic formula and find the solutions to the quadratic function. • Recall • a • Where a, b, and c are numbers • Standard form of a quadratic function.
Guiding Question: How can I find the solutions of a quadratic without graphing, factoring or completing the square? • Quadratic Formula: • Example: Solve • a = b = c =
Guiding Question: How can I find the solutions of a quadratic without graphing, factoring or completing the square? Be careful of signs, take the negative with you. • 3. • Try this • 4. • 5. What if its in vertex form? • 1. • 2.
Guiding Question: How can I find the solutions of a quadratic without graphing, factoring or completing the square? This part is called the discriminant and tells you how many solutions there are. Discriminant is positive – 2 solutions Discriminant is Zero (0) – 1 solution Discriminant is negative – No solutions
Guiding Question: How can I find the solutions of a quadratic without graphing, factoring or completing the square? • How many solutions does each problem have? • 1. • 2. • 3. • Try this, Solve
