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5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.

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Presentation on theme: "5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find."— Presentation transcript:

1 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

2 Lesson 10-4 Solving Quadratic Equations by Using the Quadratic Formula

3 Transparency 4 Click the mouse button or press the Space Bar to display the answers.

4 Transparency 4a

5 Objectives Solve quadratic equations by using the Quadratic formula Use the discriminant to determine the number of solutions for a quadratic equation

6 Vocabulary Quadratic formula – Discriminant –

7 Working Backwards Start with the answer “Undo” the operation that got you to the answer Keep “undoing” until you get back to the beginning

8 Example 1 Use two methods to solve Method 1Factoring Original equation Factor Solve for x. Zero Product Property or

9 Example 1 cont Method 2Quadratic Formula For this equation, Quadratic Formula Multiply.

10 Example 1 cont Add. Simplify. or Answer: The solution set is {–5, 7}.

11 Example 2 Solve by using the Quadratic Formula. Round to the nearest tenth if necessary. Step 1Rewrite the equation in standard form. Original equation Subtract 4 from each side Simplify.

12 Example 2 cont Step 2Apply the Quadratic Formula. Quadratic Formula a = 15, b = -8 and c = -4 Multiply, then Add. or

13 Example 2 cont Check the solutions by using the CALC menu on a graphing calculator to determine the zeros of the related quadratic function. Answer:The approximate solution set is {–0.3, 0.8}.

14 Example 3 In order to find when the ball hits the ground, you must find when H = 0. Write two equations to represent the situation on Mars and on Europa. Space Travel Two possible future destinations of astronauts are the planet Mars and a moon of the planet Jupiter, Europa. The gravitational acceleration on Mars is about 3.7 meters per second squared. On Europa, it is only 1.3 meters per second squared. Using the information and equation from Example 3 on page 548 in your textbook, find how much longer baseballs thrown on Mars and on Europa will stay above the ground than a similarly thrown baseball on Earth.

15 Example 3 cont Baseball Thrown on Mars These equations cannot be factored, and completing the square would involve a lot of computation. Baseball Thrown on Europa

16 Example 3 cont To find accurate solutions, use the Quadratic Formula. Since a negative number is not reasonable, use the positive solutions. Answer:A ball thrown on Mars will stay aloft 5.6 – 2.2 or about 3.4 seconds longer than the ball thrown on Earth. The ball thrown on Europa will stay aloft 15.6 – 2.2 or about 13.4 seconds longer than the ball thrown on Earth.

17 Example 4a State the value of the discriminant for. Then determine the number of real roots of the equation. and Simplify. Answer:The discriminant is –220. Since the discriminant is negative, the equation has no real roots.

18 Example 4b State the value of the discriminant for. Then determine the number of real roots of the equation. Step 1Rewrite the equation in standard form. Original equation Add 144 to each side Simplify. Step 2Find the discriminant. Simplify. a = 1, b = 24 and c = 144 Answer:The discriminant is 0. Since the discriminant is 0, the equation has one real root.

19 Example 4c State the value of the discriminant for. Then determine the number of real roots of the equation. Step 1Rewrite the equation in standard form. Original equation Subtract 12 from each side Simplify. Step 2Find the discriminant. Answer:The discriminant is 244. Since the discriminant is positive, the equation has two real roots. Simplify a = 3, b =10 and c = -12

20 Summary & Homework Summary: –The solutions of a quadratic equation in the form ax 2 + bx + c = 0, where a ≠ 0, are given by the Quadratic Formula: Homework: –pg -b ± √b² - 4ac x = ----------------------- 2a


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