AnswersAlgebra III ASolving Quadratic Equations: Completing the Square

Solving Quadratic Equations: Completing the Square Answers

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1
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Which quadratic equation would be used to solve for the unknown dimensions?

A
0 = 2w2
B
512 = w2
C
512 = 2w2
D
512 = 2l + 2w
2
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–32–16X 16✔ 32

A
–32
B
–16
C
X 16
D
✔ 32
3

The width of the backyard is feet.

A
–32
B
–16
C
16
D
32
4

After how many seconds does the object hit the ground?

A
2
B
4
C
8
D
16
5

Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario?

A
x2 = (2x)(x – 16)
B
x2 = (x)(x – 16)
C
x2 = (x)(x + 16)
D
x2 = (2x)(x + 16)
6

What is the value of x that makes sense in this context?

A
0 ft
B
8 ft
C
16 ft
D
32 ft
7

What are the dimensions of the new garden?

A
32 ft by 32 ft
B
64 ft by 16 ft
C
64 ft by 32 ft
D
32 ft by 16 ft

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