Factoring!
Solving Using Specific Methods
Solving Quadratics (your choice!)
Miscellaneous
Word Problems
100
Factor completely:
x^2 + 2x - 48
(x + 8)(x - 6)
100
Solve using the quadratic formula:
3x^2 + 3x - 5 = 0
x = (-3+- sqrt69)/6
100
x^2 - 7x + 12 = 0
x = 4, 3
100
Simplify:
12sqrt-108
72isqrt3
100
A rocket is launched. It's height, in meters, after t seconds is represented by the function below. What is the initial height of the object? Don't forget to include your units!
h(t) = -4.9t^2 + 19.6t + 58.8
58.8 meters
200
Factor completely:
6x^2 + 27x
3x(2x + 9)
200
Solve by factoring:
100x^2 - 1 = 0
x = 1/10, -1/10
200
Solve:
5x^2 + x + 2 = 0
x = (-1 +- isqrt(39))/10
200
What is the discriminant of this quadratic equation? State the number and type of solutions to this equation.
x^2 + 6x + 13 = 4
discriminant = 0
one real solution
200
The flight path of a rocket is modeled with the function below, where h is the height in feet and t is in seconds. What is the rocket's maximum height? Don't forget units!
h = -5t^2 + 30t + 10
55 feet
300
Factor completely:
25x^2 - 4
(5x + 2)(5x - 2)
300
Solve by graphing:
0 = 1/2(x + 4)^2 - 2
x = -6, -2
300
Solve:
-3x^2 - 96 = 0
x = +- 4isqrt2
300
What is the discriminant of this quadratic equation? State the number and type of solutions to this equation.
5x^2 - 4x - 3 = -5
discriminant = -24
two imaginary solutions
300
A rocket is launched. It's height, in meters, after t seconds is represented by the function below. What is the maximum height of the rocket? How long does it take for the rocket to reach the maximum height. Don't forget your units! Decimals are OK, if appropriate.
h(t) = -4.9t^2 + 19.6t + 58.8
Max height it 78.4 meters after 2 seconds.
400
Factor completely:
-2x^2 + 10x + 168
-2(x + 7)(x - 12)
400
Solve using the Square Root Method:
3x^2 + 144 = 0
x = +-4isqrt(3)
400
Solve:
8x^2 = 10x - 9
x = (5 +-isqrt(47))/8
400
Multiply by the complex conjuget:
-12 + 9i
225
400
A rectangular field will be fenced on all four sides. There will also be a line of fence across the field, parallel to the shorter side (see image below). 900 meters of fencing is available to use. If x represents the length of the shorter side, create an equation that represents the area of the field in terms of x.
f(x) = x((900-3x)/2)
f(x) = -3/2x^2+ 450x
500
Factor completely.
12x^2 - 34x + 24
2(2x - 3)(3x - 4)
500
Solve by completing the Square:
x^2 + 2x + 13 = 0
x = -1+-2isqrt(3)
500
Solve:
-24x^2 - 30x = -9
x = 1/4, -3/2
500
Simplify:
(-2 + 3i)(7 - 4i) - (12 + 5i)
-14 + 24i
500
A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width (x) of the pathway?
1.5 meters