Solving Quadratics by Completing the Square

The work above shows the first two steps to solve by completing the square. Which description correctly describes the error that was made?

• They needed to add -1 to both sides.

• They needed to factor out the 2 so a = 1.

• They needed to take the square root of 4 first.

• They needed to add 4 to both sides.

We are standing on the top of a 1680 ft tall building and throw a small object upward. At every second, we measure the distance of the object from the ground. Exactly t seconds after we threw the object, its height, (measured in feet) is h(t)=-16t^2+256t+1680. How long does it take for the object to reach a height of 2640 feet? Practice solving by completing the square.

• 2 & 6 seconds

• 4 & 8 seconds

• 6 & 10 seconds

• 8 & 12 seconds

On dry asphalt the distance d (in feet) needed for a car to stop is given by d=0.05s^2+1.1s where s is the car’s speed (in miles per hour). What speed limit should be posted on a road where drivers round a corner and have 80 feet to come to a stop? Round to the nearest whole number. Practice solving by completing the square.

• 52 mph

• 35 mph

• 40 mph

• 30 mph

How many solutions are there?

• 0

• 1

• 2

• Cannot be determined

Solve the following quadratics equation by completing the square... x² - 6x + 2 = 0

• x = -3 ± √7

• x = 3 ± √7

• x = 7 ± √3

• x = -7 ± √3

Solve the following quadratics equation by completing the square... x² + 2x - 5 = 0

• x = -1 ± √6

• x = 1 ± √6

• x = 6 ± √1

• x = -6 ± √1

Identify the a, b and c values for this equation:
3x² - 8x + 15 = 0

• a=3, b=8, c=0

• a=3, b=-8, c=15

• a=3, b=8, c=15

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4

• 2

• 8

• 20

Convert x²-6x+9 to factored form and identify the solution.

• (x-3)(x-3); x=3

• (x+3)(x+3); x=-3

• (x+4)(x+2); x=-4, -2

• Not factorable