Exam 8: Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

For design purposes, the large gear in the illustration is the circle . The smaller gear is a circle centered at and tangent to the larger circle. Find the equation of the smaller gear.

Graph the function.

Solve the inequality.

When a wholesaler sells CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?

Graph the function. f ( x ) = x ² + 3

Find the coordinates of the vertex of the graph of the equation. If necessary, complete the square on x to write the equation in the form y = a ( x - h ) ² + k . Do not graph the equation.

The area of a tennis court is 2,128 square feet (see illustration). The length of the court is times the width. Find the length and width of the tennis court.

Find the vertex of the parabola and graph it.

Graph the function.

Graph the function. f ( x ) = -2(( x - 3)² - 1)

Find the inverse of the given function and express it in the form . Verify the result by showing that .

Solve the equation and verify that the sum of the solutions is - and the product of the solutions is .

Solve a formula for the indicated variable. , for .

Factor the trinomial square and use the square root method to solve the equation.

Solve the inequality.

Use the method of completing the square to solve the quadratic equation.

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Find the inverse of the given function and express it in the form . Verify the result by showing that .

Graph the function. f ( x ) = 2 x ² - 5

The graph below represents a function. Use the horizontal line test to decide whether the function is one-to-one. Answer yes or no .