Question

1-4 complete the square

1. X^2+18x+[]

A.) 9
B.) 18
C.) 36
D.) 81

2. X^2-x+[]

A.) 1
B.) -1
C.) 1/4
D.) -1/2

3. X^2-24x+[]

A.) 6
B.) 12
C.) 144
D.) -72

4. M^2-3m+[]

A.) 3
B.) 9
C.) 2/3
D.) 9/4

5. For a fence that uses 100 feet of fencing to be built around a rectangular garden, the area is given by A=50x-x^2, where x is the length in feet. Find the dimensions of the garden with the maximum area.

A.) length 50, with 10
B.) length 25, with 25
C.) length 50, with 25
D.) length 30, with 20

Answer 1

D, C, C and D

Since the coefficient of the x² term is 1 in all 3 quadratics

To complete the square add (half the coefficient of the x-term )²

1. x² + 18x

add ($\frac{18}{2}$)² = 9² = 81 → D

2. x² - x

add ($\frac{-1}{2}$)² = $\frac{1}{4}$ → C

3. x² - 24x

add ($\frac{-24}{2}$)² = (- 12 )² = 144 → C

4. m² - 3m

add($\frac{-3}{2}$)² = $\frac{9}{4}$ → D