Unit Test — Unit test Answers

Use completing the square to solve for in the equation .

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan?A = lw

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is the area of the original square. What was the side length of the original square?A = s2

What is one of the solutions to the following system?

Which equation has a graph that lies entirely above the x-axis?

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by , where x and y are measured in inches. Where is the focus of the flashlight?

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film the person between 15 m and 10 m above the ground. For which interval of time should the camera film the person?

Which system is equivalent to ?

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

Solve for in the equation .

Which equation demonstrates the multiplicative identity property?

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

Which equation represents a graph with a vertex at (–3, 2)?

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

When a baseball is hit by a batter, the height of the ball, h(t), at time t, , is determined by the equation . If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

A company plans to sell pens for $2 each. The company’s financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by , where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?