Quadratics WKST

Quadratics WKST

–9

Quadratics WKST

(x)2 + 1

Worksheet Key1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

7 2 3x x

26 5 9x x

3 6x x x

2 21 5x x

22 2 5x x x

3 29 6 2 1x x x

2 1 1x x

2 2 7x x x

25 3 2x x

5 1 5 1 4x x x

2 25 5x x

3 7 4 5y x

13. 4 5 6 7 3x y x

x

x

EXAMPLE 10

A town has a nature preserve with a rectangular field that measures 600 meters by 400 meters. The town wants to double the area of the field by adding land as shown. What are the dimensions of the field?

600 m

400 m

A lw 600 400A

240,000 600 400

2 240,000 600 400x x 2480,000 240,000 1,000x x

20 1,000 240,000x x

04/19/2023 11:06 PM 4.3: Factoring and Solving when a = 1 5

x

x

EXAMPLE 10

A town has a nature preserve with a rectangular field that measures 600 meters by 400 meters. The town wants to double the area of the field by adding land as shown. What are the dimensions of the field?

600 m

400 m

20 1,000 240,000x x 0 200 1200x x

200 0x 1200 0x 200, 1200x

800 600m m04/19/2023 11:06 PM 4.3: Factoring and Solving when a = 1 6

Section 4.4

04/19/2023 11:06 PM 75.3 - Solving Quadratic Equations by Factoring

Solving Quadratic Equations when a > 1 and by factoring with GCF

Factoring Steps when a>1A. Make sure the equation is all on ONE sideB. Determine if there is a GCFC. Determine the Target Product and Target Sum of the

equation1. Multiply the First and Last Term2. Ensure the terms adds to the middle and multiplies the end3. Rewrite the problem with the new middle terms4. Make sure that one of the binomials is the same on both sides

D. Factor by Grouping by Splitting the TermsE. Combine like terms and multiply

Example 1Factor 2x2 + 5x + 2

SUM PRO

DU

CT

22 5 2x x Sum: 5

Product: +4

1, 4

2, 2

2, 2

1, 4

+4What number adds up to +5 and multiplies to +4

Example 1Factor 2x2 + 5x + 2

22 1 4 2x x x 2 1x x 2 2 1x

2 2 1x x

22 5 2x x Sum: 5

Product: +4

You must add an X to the middle term

because it has to match the original equation

This sign should ALWAYS be bought

down

Example 2Factor 3x2 + 20x – 7

3 1 7x x

Example 3Factor 2x2 – 9 – 3x

2 3 3x x

Factor 4x2 + 4x – 3

2 3 2 1x x

Your Turn

Solve 3x2 + 10x – 8 = 0

Example 4

23 10 8x x Sum: 10

Product: 24

24

3 2 4 0x x

24,

3

23 2 12 8x x x

Don’t forget the xy in the

middle

3 2 0x 4 0x

Solve 5x2 – 27x = 18

Example 5

3,6

5

Solve 4x2 – 10x + 15 = 10x – 10

Your Turn

5

2DR

Solve 16x2 – 1 = 0

Example 6

216 1x Sum: 10

Product: 24

16

4 4 1 4 1x x x

1

4

216 4 4 1x x x

Don’t forget the xy in the

middle

4 1 0x 4 1 0x

Solve 9x2 – 64 = 0

Example 7

8

3

Solve 36x2 – 9 = 0

Your Turn

1

2

Factor 8x2 – 14xy + 3y2

Example 8

2 28 14 3x xy y Sum: 14

Product: +24

+242 28 12 2 3x x x y 4 2 3x x y 2 3y x y 4 2 3x y x y

2 28 12 2 3x xy xy y

Don’t forget the xy in the

middle

Factor 6xy2 + 33xy – 18x…

3 2 1 6x y y

Your Turn

You have made a rectangular quilt that is 5 feet by 4 feet. You want to use the remaining 10 square feet of fabric to add border of uniform width to the quilt. What should the width of the quilt’s border be?

Example 9

4 2x

5 2x

You have made a rectangular quilt that is 5 feet by 4 feet. You want to use the remaining 10 square feet of fabric to add border of uniform width to the quilt. What should the width of the quilt’s border be?

Example 9

4 2x

5 2x

Area of Quilt Border - Area of Quilt = Area of border

5 2 4 2x x 5 4 10 5 2 4 2 20 10x x

220 18 4 20 10x x 24 18 10 0x x

22 2 9 5 0x x

2 2 1 5 0x x

1: 5

2ext

5 6 x in

Page 2633-19 EOO, 23-29 odd, 33-57 EOO

Assignment