Exam 8: Quadratics and the Mathematics of Motion

Select the choice which best describes the graph of .

Find a function for the average rate of change of the function .

The height, h, of a toy rocket t seconds after launch is given by the function . A) Find the time (in seconds) when the rocket reaches the maximum height. B) Find the maximum height (in feet) of the rocket.Round values to 2 decimal places, if necessary.

For the following function, will the vertex be above, below, or on the x-axis?

A ball is launched vertically into the air from a slingshot set at ground level. If the ball reaches a maximum height of 176.4 m, what must the initial velocity have been?

The daily profit (f), in dollars, of a small business is given by the function, , where x represents the total number of units sold. How many units does the business need to sell in order to maximize the daily profit?

After 3 seconds, a falling object has a velocity of 3,023 cm/sec. Find the equation to describe the velocity of the object at t seconds. Assume that g = 980 cm/sec².

A free falling body has an initial velocity of 7 m/sec. Find the equation to describe the velocity of the object at time t seconds. Assume that g = 9.8 m/sec².

Find the minimum value of the function . Round values to 2 decimal places, if necessary.

Find the vertex of the parabola

Create a quadratic equation of the form , where a = 0.5 and (h, k) = (-1, -7).

Convert the function into vertex form, , by completing the square.

Transform the function into a new function by stretching by a factor of 3 and reflecting across the x-axis, and then shifting the result down 3 units. Find the equation of .

For the quadratic function pictured determine the x-coordinates of its horizontal intercepts. (Enter the values in numerical order separated by a comma.)

Determine whether this parabola is concave up or down.

Convert the function into vertex form, , by completing the square.

Find a for the parabola , whose focus is located at

The daily profit (f), in dollars, of a small business is given by the function, , where x represents the total number of units sold. What is the maximum daily profit of the business?

For the data in the table below calculate the average rate of change and the average rate of change of the average rate of change to determine whether the function is linear, exponential, or quadratic.

At t = 0, a ball is thrown upward at a velocity of 320 ft/sec from the top of a building 800 ft high. The ball's height is measured in feet above the ground. Assuming the height at t = 0 is 0 ft, at what time does the ball reach the ground? Round the answer to 2 decimal places if necessary.