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Section 9.3- Solving Quadratic Equations Essential Question: How is graphing a quadratic equation similar to solving it algebraically? Do Now: 1. Use the equation below and solve it using two different methods. 𝑥 2 − 25 = 0 a. Solve the equation below by factoring. b. Solve the same equation using a different algebraic method. 2. Can you take the square root of each number? Explain. a. √49 b. √−49 Solving Quadratic Equations by Graphing The solutions to a quadratic equation represent the ____________________________. There are three cases when graphing quadratic equations. o A parabola can have AT ____________, _____ solutions. o It may also only have _______________________________. o There may also be instances where there is __________ _______________. This means there are no _________________________________. Example 1: Solving by Graphing Graph the following quadratic functions. What are the solutions of each equation? a. 𝑦 = 𝑥 2 − 16 Solutions: _______________________ c. 𝑦 = 𝑥 2 + 1 Solutions: _______________________ b. 𝑦 = 𝑥 2 Solutions: _______________________ d. 𝑦 = 𝑥 2 − 1 Solutions: _______________________ Example 2: Solving Using Square Roots What are the solutions of each equation? 1 2 𝑥 4 a. 3𝑥 2 − 75 = 0 b. c. 𝑥 2 − 36 = −36 d. 3𝑥 2 + 15 = 0 Example 3: Choosing a Reasonable Solution −1=0 Group Work: Solve each equation by graphing the related function OR by finding square roots. 1. 𝑥 2 − 25 = 0 3. 2 2 𝑥 3 −6=0 2. 2𝑥 2 − 8 = 0 4. 𝑥 2 + 36 = 0 5. You have enough paint to cover an area of 50 𝑓𝑡 2 . What is the side length of the largest square that you could paint? Round your answer to the nearest tenth of a foot. 6. What do you notice about all of the values for ‘b’ when you are able to solve a quadratic equation using square roots? HW: p. 564 #9-17 odds, 20-28 evens, 40