evaluate the expression
DESCRIPTION
2. 1. ANSWER. 2. 4. 49. 3. 9. 25. 7. 2. 2. 5. ANSWER. Evaluate the expression. 3. An acorn falls to the ground from a height of 25 feet. How long was the acorn in the air?. 1.25 sec. ANSWER. Evaluate the expression. 25. 5. 2. c =. =. 4. 2. EXAMPLE 1. - PowerPoint PPT PresentationTRANSCRIPT
Warm-Up Exercises
Evaluate the expression.
1. 23
2
2. 75
2
ANSWER49
ANSWER4925
Warm-Up Exercises
ANSWER 1.25 sec
Evaluate the expression.
An acorn falls to the ground from a height of 25 feet. How long was the acorn in the air?
3.
Warm-Up ExercisesEXAMPLE 1 Complete the square
Find the value of c that makes the expression x2 + 5x + c a perfect square trinomial. Then write the expression as the square of a binomial.
STEP 1Find the value of c. For the expression to be a perfect square trinomial, c needs to be the square of half the coefficient of bx.
Find the square of half the coefficient of bx.2
2 = 254c = 5
Warm-Up ExercisesEXAMPLE 1 Complete the square
STEP 2Write the expression as a perfect square trinomial. Then write the expression as the square of a binomial.
Substitute 25 for c.
4
x2 + 5x + c = x2 + 5x +254
Square of a binomial52
2+x =
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.
1. x2 + 8x + c ANSWER 16; (x + 4)2
2. x2 12x + c
3. x2 + 3x + c
ANSWER 36; (x 6)2
ANSWER ; (x )294
32
Warm-Up ExercisesEXAMPLE 2 Solve a quadratic equation
Solve x2 – 16x = –15 by completing the square.
SOLUTION
Write original equation.x2 – 16x = –15
Add , or (– 8)2, to each side.
– 16 2
2
x2 – 16x + (– 8)2 = –15 + (– 8)2
Write left side as the square of a binomial.
(x – 8)2 = –15 + (– 8)2
Simplify the right side.(x – 8)2 = 49
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
Take square roots of each side.x – 8 = ±7
Add 8 to each side.x = 8 ± 7
ANSWER
The solutions of the equation are 8 + 7 = 15 and 8 – 7 = 1.
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
CHECK
You can check the solutions in the original equation.
If x = 15:
(15)2 – 16(15) –15 ?=
–15 = –15
If x = 1:
(1)2 – 16(1) –15 ?=
–15 = –15
Warm-Up ExercisesEXAMPLE 3 Solve a quadratic equation in standard form
Solve 2x2 + 20x – 8 = 0 by completing the square.
SOLUTION
Write original equation.2x2 + 20x – 8 = 0
Add 8 to each side.2x2 + 20x = 8
Divide each side by 2.x2 + 10x = 4
Add 10 2
2, or 52, to each side.x2 + 10x + 52 = 4 + 52
Write left side as the square of a binomial.
(x + 5)2 = 29
Warm-Up ExercisesEXAMPLE 3 Solve a quadratic equation in standard form
Take square roots of each side.x + 5 =
± 29
Subtract 5 from each side.x = –5 ± 29
ANSWER
The solutions are – 5 + 29 0.39 and – 5 – 29 –10.39.
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
4. x2 – 2x = 3
ANSWER 1, 3
5. m2 + 10m = –8
ANSWER 9.12, 0.88
6. 3g2 – 24g + 27 = 0
ANSWER 1.35, 6.65
Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem
CRAFTS
You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform border as shown. You have enough chalkboard paint to cover 6 square feet. Find the width of the border to the nearest inch.
Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem
SOLUTION
STEP 1
Write a verbal model. Then write an equation. Let x be the width (in feet) of the border.
6 = (7 – 2x) (3 – 2x)
Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem
STEP 2Solve the equation.
Write equation.6 = (7 – 2x)(3 – 2x)
Multiply binomials.6 = 21 – 20x + 4x2
Subtract 21 from each side.–15 = 4x2 – 20x
Divide each side by 4. – = x2 – 5x154
Add –52
, or 25 4
, to each side.225 4– 15
4 + = x2 – 5x + 25 4
Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem
Write right side as the square of a binomial.
– 15 4 +
25 4 = (x – )25
2
Simplify left side.52 = (x – )5
22
Take square roots of each side. ± 52
= x – 52
Add 52
to each side.52 ± 5
2 = x
Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem
The solutions of the equation are
and It is not possible for the width
of the border to be 4.08 feet because the width of the door is 3 feet. So, the width of the border is 0.92 foot. Convert 0.92 foot to inches.
52
52+ 4.08
52
52 0.92
0.92 ft 12 in.1 ft = 11.04 in Multiply by conversion factor
ANSWER
The width of the border should be about 11 inches.
Warm-Up ExercisesGUIDED PRACTICE for Example 4
7. WHAT IF? In Example 4, suppose you have enough chalkboard paint to cover 4 square feet. Find the width of the border to the border to the nearest inch.
ANSWER
The width of the border should be about 13 inches.
Warm-Up Exercises
ANSWER – 1.29, 9.29
ANSWER –14, 2
Daily Homework Quiz
1. x2 + 12x = 28
Solve the equation by completing the square. Round to the nearest hundredth, if necessary.
2. m2 – 8m = 12
Warm-Up ExercisesDaily Homework Quiz
What is the width of the border that surrounds this poster?
3.
ANSWER 1 in