Exam 10: Completing the Square

Suppose a deposit of $3,500 in a savings account that paid an annual interest rate r (compounded yearly) is worth $4,098 after 2 years. Using the formula , we have Solve for r to find the annual interest rate. Round the answer to the nearest tenth. r = __________%

Solve the following equation. Remember, if you square both sides of an equation in the process of solving it, you have to check all solutions in the original equation.

Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) x = __________

Solve for by using the quadratic formula with , , and .

Multiply both sides of the equation by their LCD. Then solve the resulting equation.

Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square. _____ _____

Solve the equation. x = __________

Look for the greatest common factor, then use the quadratic formula to find all solutions.

Solve the inequality and graph the solution set.

Solve the inequality and graph the solution set.

Determine all solutions for . k = __________

Find the coordinates of the vertex, and indicate whether the vertex is the highest point on the graph or the lowest point on the graph.

Use the discriminant to find the number and kind of solutions for the following equation. Discriminant __________ How many solutions does the equation have? __________ What kind of solutions are they? __________

For the equation, find the coordinates of the vertex, and indicate whether the vertex is the highest point on the graph or the lowest point on the graph.

Writing in 1829, former President James Madison made some predictions about the growth of the population of the United States. The populations he predicted fit the equation where y is the population in millions of people x years from 1829. Use the equation to determine the approximate year President Madison would have predicted that the U.S. population would reach 100,000,000. Round answer to the nearest year.

Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) r = __________

Solve the equation using the quadratic formula. x = __________

Use the discriminant to find the number and kind of solutions for the following equation. Discriminant __________ How many solutions does the equation have? __________ What kind of solutions are they? __________

Fill in the blanks so that the left side of each is a perfect square trinomial; that is, complete the square. _____ _____

Find the vertex and any two convenient points to choose the graph of the following equation.