algebra ii - solving quadratic equations by factoring

The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t - 16t^2. How long after launch does the projectile return to the ground? a) 2 seconds b) 4 seconds c) 14 seconds d) 16 seconds

a) 2 seconds

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation? a) k(x-2)(x-7)=0 b) (x-2)(x-7)+k=0 c) (x+2)(x+7)+k=0 d) k(x+2)(x+7)=0

a) k(x-2)(x-7)=0

Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12. a) x = -6 or x = 1 b) x = -3 or x = -2 c) x = -1 or x = 6 d) x = 2 or x = 3

a) x = -6 or x = 1

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased? a) 2 ft b) 4 ft c) 8 ft d) 10 ft

b) 4 ft

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle? a) 20 in. b) 26 in. c) 120 in. d) 138 in.

c) 120 in.

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x - 2x^2. For what number of tabletops does the company make a profit of $0? a) 100 tabletops b) 120 tabletops c) 240 tabletops d) 480 tabletops

c) 240 tabletops

What are the solutions to the equation (x - 6)(x + 8) = 0? a) x = -6 or x = 8 b) x = -6 or x = -8 c) x = 6 or x = -8 d) x = 6 or x = 8

c) x = 6 or x = -8

What are the solutions to the equation (2x - 5)(3x - 1) = 0? a) x=-5/2 or x=-1/3 b) x=2/3 or x=3 c) x=5/2 or x=1/3 d) x=5 or x=1

c) x=5/2 or x=1/3

A rectangular field has an area of 1,764 m^2. The width of the field is 13 m more than the length. What is the perimeter of the field? a) 121 m b) 144 m c) 168 m d) 170 m

d) 170 m

The square of 9 less than a number is 3 less than the number. What is the number? a) -12 or 7 b) -12 or -7 c) -7 or 12 d) 7 or 12

d) 7 or 12

A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What does the value of x in her solutions represent? a) one possible length and one possible width b) two possible amounts for the widths c) two possible amounts for the lengths d) two possible amounts by which the dimensions were changed

d) two possible amounts by which the dimensions were changed

Use the zero product property to find the solutions to the equation x^2 - 13x + 30 = 0. a) x = -10 or x = -3 b) x = -10 or x = 3 c) x = -3 or x = 10 d) x = 3 or x = 10

d) x = 3 or x = 10

Use the zero product property to find the solutions to the equation x^2 + 12 = 7x. a) x = -4 or x = 3 b) x = -4 or x = -3 c) x = -3 or x = 4 d) x = 3 or x = 4

d) x = 3 or x = 4

What are the solutions to the equation 3(x - 4)(x + 5) = 0? a) x = -4 or x = 5 b) x = 3, x = 4, or x = -5 c) x = 3, x = -4, or x = 5 d) x = 4 or x = -5

d) x = 4 or x = -5