Exam 5: Quadratic Functions and Models

If represents John s salary per month (in thousands of dollars) after working number of months at a certain job, which one of the following would describe the meaning of ?

Express in the standard form of a quadratic function.

Which one of the following functions describes a function f whose graph is a parabola with the vertex and passes through the point ?

Sam has 600 ft of fencing to fence in a rectangular garden. Find a function A that models the area of the garden in terms of the width of the garden and determine the maximum area of the garden and the corresponding width of the garden to attain this maximum area.

Solve the equation using the Quadratic Formula.

Using the graph below, find the x -value at which the maximum value of the function occurs.

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . What is the maximum height attained by the ball, and after how many seconds is that height attained?

Using the data provided, create a quadratic model that best fits the data.

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 500 m apart, and the lowest point of the suspension cables is 120 m below the top of the towers, as shown below. Find a quadratic function that models the parabolic part of the cables, placing the origin of the coordinate axes at the vertex.

Find the minimum value and the corresponding x -value at which the minimum occurs for the function .

A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool. Which one of the following is an appropriate scatterplot for this data?

Which one of the following graphs illustrate the function ?

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . Does the ball reach a height of 251 feet?