Radical Zeros. Lesson #5 of Unit 1: Quadratic Functions and Factoring Methods (Textbook Ch1.5)

Transcription

1 Radical Zeros Lesson #5 of Unit 1: Quadratic Functions and Factoring Methods (Textbook Ch1.5)

2 Learner Goals 1. Evaluate and approximate square roots 2. Solve quadratic equations by finding square roots.

3 Text p.32 Terminology of Radical Numbers Square root is any number that is two identical factors of a product, and it s denoted as below Radical Sign: is the symbol which denotes the number of identical factors you are searching for. Radical Radicand: Number under the radical sign that you are breaking down. Radical is the combination of a radical sign and a radicand

4 Text p.32 Properties of Square Roots EXAMPLES:

5 Text p.32 Simplifying Square Roots 1/2 Simplification Rule #1 No perfect square factor in the radicand. ex) Simplify the expression.

6 Text p.33 Simplifying Square Roots 2/2 Simplification Rule #2 No radicals in the denominator of a fraction. The process of eliminating the racial from the denominator is called rationalizing the denominator. ex) Simplify the expression. Conjugates

7 Group Discussion 1 Let. 1) Find y when x = 3, and when x = -3. 2) Simplify, and. 3) What are the roots of equation? 4) Is it possible to find the roots of equation? If impossible, explain why not.

8 Suggested Problems 1 Workbook p.11 1, 3, 5, 7, 10, 11

9 Solving Quadratic Equations by Finding Square Roots 1/2 Text p.33 If b = 0 for the equation ax 2 +bx + c = d, then ax 2 + c = d. To solve this equation, we isolate x 2 term, so we have x 2 = (d c)/a. As long as (d c)/a is a positive number, our solution for the equation is x =. ex) (read as plus or minus ) Solve each of the following equations. a) x = 0 b) 25y 2 3 = 0 c) 7r 2 10 = 25 d)

10 Solving Quadratic Equations by Finding Square Roots 2/2 Text p.34 If you are given an equation in the form of a(x h) 2 + k = d, then we isolate (x h) 2 first, so we have (x h) 2 = (d k)/a. As long as (d k)/a is a positive number,. Then our solution for the equation is.. ex) Solve each of the following equations. a) (x 7) 2 = 81 b) (x + 3) 2 = 24 c) 4(x 1) 2 = 8 d) 7(x 4) 2 18 = 10

11 Guide on Steps Step 1 - Isolate the perfect square that contains the variable Step 2 - Take the square root of both sides of the equation Step 3 - Include a +/- symbol on the right to solve for both answers Step 4 - simplify and solve for the variable Step 5 - check your answers by simply plug back into the given question

12 Text p.35 Group Discussion 2 An engineering student is in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. When an object is dropped, its height h (in feet) above the ground after t seconds, and s is the initial height, can be modeled by the function, 2 h 16t s To the nearest tenth of a second, about how long will it take for the egg s container to hit the ground? Assume there is no air resistance.

13 The question asks to find the time it takes for the container to hit the ground. Initial height (s) = 32 feet Group Discussion 2 Solution Height when its ground (h) = 0 feet Time it takes to hit ground (t) = unknown 16t The given model is. h 2 s

14 Group Discussion 2 Solution Substitute numbers into the model. 0 = -16t = -16t = -16t 2-32 / -16 = -16t 2 / = t 2 t = 2 seconds or approx. 1.4 seconds

15 Text p.35 Practice A cliff diver dives off a cliff 40 feet above water. His height after t seconds is 2 given by the model, h 16t s. 1) Find the diver s height after 1 second. 2) Find the time for the diver to hit the water.

16 Suggested Problems 2 Solve each of the following equations. 1) z 2 72 = 0 2) x = 7 3) (y + 9) 2 = 121 4) (x 8) 2 = 128 5) (x + 5) 2 = -4 6) 2x 2 15 = 35 7) 3(x 2) = 22 8)