1. The following two equations describe the height of a missile above (or below) the surface of the ocean, when it is launched from a submarine:

1. $ y = -t^2 + 12t - 20 $
2. $ y = -5t^2 + 30t - 20$

2. After how many seconds will each missile break through the surface of the water?
3. After ...

Factoring with quadratic equation

Factoring

Determine what values of x will make y equal to zero:

1. $y = x^2 + 8x + 16$
2. $y = x^2 - 4x - 32$
3. $y = x^2 - 7x + 12$
4. $y = 2x^3 -10x^2 - 28x$

Turn the following into equations:

1. A runner starts running toward Westerly from Providence (60 miles away), going a steady 10 miles per hour.  Make an equation that gives their distance from Providence.
2. A number is 12 more than the product of the number and -5.  What is the number?
3. A ...

Operations with polynomials

Exponent rules

1. Simplify the following expressions:
   1. $(\frac{7}{9})^0$
   2. $y^{-2}y^{-5}$
   3. $(-xy^2)^{-4}$
   4. $(y^3y^4)^4$
   5. $y^2y^5$
2. Bacteria grow by doubling every 10 minutes. Suppose you are infected by one bacteria, and allow it to grow for 4 hours. Then you begin frantically washing and ...

Write equations representing each of the following (don't solve):

1. Three more than twice a number is 100
2. A number multiplied by itself is 16 less than 52
3. The product of two numbers is 5 more than their sum
4. Find the next number in the sequence: 1, 4, 7, 10, ...

Mini-project on graphing and solving systems of equations

1. The sum of two numbers is -18. One number is 2 greater than three times the other. Turn both sentences into equations, then find the two numbers.

Practicing systems of equations

1. A bicyclist goes at a steady 25 miles per hour, leaving 1 hour after a runner, who maintains a steady 14 miles per hour. Graph the two, find the equations that describe their motion, and solve to determine at what time the bicyclist will catch the runner
2. Graph this equation ...

Solving pursuit problems

1. If Santa Claus delivers presents to one child per minute, how many hours would it take him to get to every child on earth? Make reasonable estimates for any numbers you need, write them down clearly, and show all your work -- no calculators, phones, tablets, etc. allowed (but feel free ...

Using graphs to solve systems of equations

1. If you have an order for 84 cakes, and one employee who can make 3 per hour, and a second who can make 4 per hour, how many hours will it take to fill the order?

Graphing