WarmUp Exercises Evaluate the expression 1 49 ANSWER

  • Slides: 23
Download presentation
Warm-Up Exercises Evaluate the expression. 1. – √ 49 ANSWER – 7 2. √

Warm-Up Exercises Evaluate the expression. 1. – √ 49 ANSWER – 7 2. √ 200 ANSWER about 14. 1

Warm-Up Exercises Evaluate the expression. 3. ± √ 121 ANSWER ± 11 4. A

Warm-Up Exercises Evaluate the expression. 3. ± √ 121 ANSWER ± 11 4. A ball is dropped from a height 9 feet above the ground. How long does it take the ball to hit the ground? ANSWER 0. 75 sec

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations Solve the equation. . a 2 x

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations Solve the equation. . a 2 x 2 = 8 SOLUTION a. 2 x 2 = 8 x 2 = 4 x = ± 4 = ± 2 Write original equation. Divide each side by 2. Take square roots of each side. Simplify. . ANSWER The solutions are – 2 and 2

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations b. m 2 – 18 = –

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations b. m 2 – 18 = – 18 m 2 = 0 m= 0 ANSWER The solution is 0. Write original equation. Add 18 to each side. The square root of 0 is 0.

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations c. b 2 + 12 = 5

EXAMPLE Warm-Up 1 Exercises Solve quadratic equations c. b 2 + 12 = 5 b 2 = – 7 Write original equation. Subtract 12 from each side. ANSWER Negative real numbers do not have real square roots. So, there is no solution.

EXAMPLE Warm-Up 2 Exercises Take square roots of a fraction Solve 4 z 2

EXAMPLE Warm-Up 2 Exercises Take square roots of a fraction Solve 4 z 2 = 9. SOLUTION 4 z 2 = 9 Write original equation. 9 z 2 = 4 z=± 3 2 Divide each side by 4. 9 4 Take square roots of each side. Simplify.

EXAMPLE Warm-Up 2 Exercises Take square roots of a fraction ANSWER The solutions are

EXAMPLE Warm-Up 2 Exercises Take square roots of a fraction ANSWER The solutions are – 3 and 3 2 2

EXAMPLE Warm-Up 3 Exercises Approximate solutions of a quadratic equation Solve 3 x 2

EXAMPLE Warm-Up 3 Exercises Approximate solutions of a quadratic equation Solve 3 x 2 – 11 = 7. Round the solutions to the nearest hundredth. SOLUTION 3 x 2 – 11 = 7 Write original equation. 3 x 2 = 18 Add 11 to each side. x 2 = 6 Divide each side by 3. x = ± 6 Take square roots of each side.

EXAMPLE Warm-Up 3 Exercises Approximate solutions of a quadratic equation x ± 2. 45

EXAMPLE Warm-Up 3 Exercises Approximate solutions of a quadratic equation x ± 2. 45 Use a calculator. Round to the nearest hundredth. ANSWER The solutions are about – 2. 45 and about 2. 45.

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 1. c 2 – 25 = 0 ANSWER – 5, 5. 2. 5 w 2 + 12 = – 8 ANSWER no solution ANSWER 0 3. 2 x 2 + 11 = 11

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 4. 25 x 2 = 16 ANSWER – 4 5 4 , 5 5. 9 m 2 = 100 ANSWER – 10 10 3 , 3 6. 49 b 2 + 64 = 0 ANSWER no solution

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED

EXAMPLE 1 Exercises Warm-Up for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. Round the solutions to the nearest hundredth. 7. x 2 + 4 = 14 ANSWER – 3. 16, 3. 16 8. 3 k 2 – 1 = 0 ANSWER – 0. 58, 0. 58 9. 2 p 2 – 7 = 2 ANSWER – 2. 12, 2. 12

EXAMPLE Warm-Up 4 Exercises Solve a quadratic equation Solve 6(x – 4)2 = 42.

EXAMPLE Warm-Up 4 Exercises Solve a quadratic equation Solve 6(x – 4)2 = 42. Round the solutions to the nearest hundredth. 6(x – 4)2 = 42 (x – 4)2 = 7 x – 4 = ± 7 x = 4 ± 7 Write original equation. Divide each side by 6. Take square roots of each side. Add 4 to each side. ANSWER The solutions are 4 + 7 6. 65 and 4 – 7 1. 35.

EXAMPLE Warm-Up 4 Exercises Solve a quadratic equation CHECK To check the solutions, first

EXAMPLE Warm-Up 4 Exercises Solve a quadratic equation CHECK To check the solutions, first write the equation so that 0 is on one side as follows: 6(x – 4)2 – 42 = 0. Then graph the related function y = 6(x – 4)2 – 42. The x-intercepts appear to be about 6. 6 and about 1. 3. So, each solution checks.

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem SPORTS EVENT During an ice hockey

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem SPORTS EVENT During an ice hockey game, a remotecontrolled blimp flies above the crowd and drops a numbered tabletennis ball. The number on the ball corresponds to a prize. Use the information in the diagram to find the amount of time that the ball is in the air.

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem SOLUTION STEP 1 Use the vertical

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem SOLUTION STEP 1 Use the vertical motion model to write an equation for the height h (in feet) of the ball as a function of time t (in seconds).

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem h = – 16 t 2

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem h = – 16 t 2 + vt + s Vertical motion model h = – 16 t 2 + 0 t + 45 Substitute for v and s. STEP 2 Find the amount of time the ball is in the air by substituting 17 for h and solving for t.

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem h = – 16 t 2

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem h = – 16 t 2 + 45 17 = – 16 t 2 + 45 – 28 = – 16 t 2 Write model. Substitute 17 for h. Subtract 45 from each side. 28 = t 2 16 Divide each side by 16. 28 =t 16 Take positive square root. 1. 32 t Use a calculator.

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem ANSWER The ball is in the

EXAMPLE Warm-Up 5 Exercises Solve a multi-step problem ANSWER The ball is in the air for about 1. 32 seconds

EXAMPLE 1 Exercises Warm-Up for Examples 4 and 5 Solve quadratic equations GUIDED PRACTICE

EXAMPLE 1 Exercises Warm-Up for Examples 4 and 5 Solve quadratic equations GUIDED PRACTICE Solve the equation. Round the solution to the nearest hundredth if necessary. 10. 2(x – 2)2 = 18 ANSWER – 1, 5 11. 4(q – 3)2 = 28 ANSWER 0. 35, 5. 65 12. 3(t + 5)2 = 24 ANSWER – 7. 83, – 2. 17

EXAMPLE 1 Exercises Warm-Up for Examples 4 and 5 Solve quadratic equations GUIDED PRACTICE

EXAMPLE 1 Exercises Warm-Up for Examples 4 and 5 Solve quadratic equations GUIDED PRACTICE 13. WHAT IF? In Example 5, suppose the table-tennis ball is released 58 feet above the ground and is caught 12 feet above the ground. Find the amount of time that the ball is in the air. Round your answer to the nearest hundredth of a second. ANSWER The ball is in the are for about 1. 70 second.

Daily Homework Quiz Warm-Up Exercises Solve the equation. Round solutions to the nearest hundredth,

Daily Homework Quiz Warm-Up Exercises Solve the equation. Round solutions to the nearest hundredth, if necessary. 1. 4 b 2 – 13 = 3 ANSWER – 2, 2 2. 9 x 2 = 25 ANSWER – 5 , 5 3 3 3. 3 n 2 – 18 = 12 ANSWER – 3. 16, 3. 16

Daily Homework Quiz Warm-Up Exercises 4. At a football game you are sitting 32

Daily Homework Quiz Warm-Up Exercises 4. At a football game you are sitting 32 feet above the ground. If your hat comes off falls to the ground, how long will it be in the air? ANSWER About 1. 41 sec

WarmUp Exercises 1 Evaluate ANSWER 2 Evaluate ANSWERWarmUp Exercises 1 Evaluate ANSWER 2 Evaluate ANSWER
WarmUp Exercises Evaluate the expression when x 4WarmUp Exercises Evaluate the expression when x 4
WarmUp Exercises Evaluate each expression 1 10 22WarmUp Exercises Evaluate each expression 1 10 22
WarmUp Exercises Evaluate the expression when x 4WarmUp Exercises Evaluate the expression when x 4
WarmUp Exercises WarmUp In Exercises 1 and 2WarmUp Exercises WarmUp In Exercises 1 and 2
WarmUp Exercises WarmUp In Exercises 1 and 2WarmUp Exercises WarmUp In Exercises 1 and 2
WarmUp Exercises WARMUP PROBLEM Simplify the expression AssumeWarmUp Exercises WARMUP PROBLEM Simplify the expression Assume
Relations Exercises Exercises In the exercises below takeRelations Exercises Exercises In the exercises below take
Warmup Warmup Warmup Warmup Agenda n n nWarmup Warmup Warmup Warmup Agenda n n n
Station 1 Evaluate Each Expression 1 Evaluate 2Station 1 Evaluate Each Expression 1 Evaluate 2
EXAMPLE 1 Evaluate expressions Evaluate the expression 27EXAMPLE 1 Evaluate expressions Evaluate the expression 27
WarmUp Exercises Use this diagram for Exercises 1WarmUp Exercises Use this diagram for Exercises 1
WarmUp Exercises In Exercises 1 4 use A0WarmUp Exercises In Exercises 1 4 use A0
WarmUp Exercises Use this diagram for Exercises 1WarmUp Exercises Use this diagram for Exercises 1
WarmUp Exercises In Exercises 1 4 use A0WarmUp Exercises In Exercises 1 4 use A0
WarmUp Exercises Use this diagram for Exercises 1WarmUp Exercises Use this diagram for Exercises 1
WarmUp Exercises In Exercises 1 4 use A0WarmUp Exercises In Exercises 1 4 use A0
WarmUp Exercises 2 5 4 Evaluate cos 60WarmUp Exercises 2 5 4 Evaluate cos 60
WarmUp Exercises Evaluate the logarithm 1 log 5WarmUp Exercises Evaluate the logarithm 1 log 5
WarmUp Exercises 1 Evaluate 3 x 5 yWarmUp Exercises 1 Evaluate 3 x 5 y
WarmUp Exercises 1 Evaluate 3 x 5 yWarmUp Exercises 1 Evaluate 3 x 5 y
WarmUp Exercises ab 1 Evaluate if a 5WarmUp Exercises ab 1 Evaluate if a 5