Exam 3: Quadratic Functions

The height of a baseball in feet seconds after it has been hit is given by . a) What is the height of the ball 0.2 seconds after it was hit? b) When does the ball hit the ground? (If necessary, round your answer to three decimal places)

Find a quadratic equation, , with zeros at and such that .

Suppose a quadratic function has vertex (5, 0) and has y-intercept 2. Its formula can be written , where a = _____, and b = _____.

How many distinct real roots does the function have?

A relief package is dropped from an airplane and falls to the ground along a parabolic path, starting at the vertex of the parabola. The package was released when the plane was directly above a marker at a height of 4 kilometers, and the package hits the ground 4.47 kilometers from the marker. If h is the height of the package when it is a horizontal distance d from the marker, the equation for h in terms of d is given by , where a = _____, b = _____, and c = _____. Round any decimals to 3 places.

The height of an object above the ground is described by the function . a) What is the initial height of the object at time t= 0? b) When does the object have height 3?

Find a formula in terms of For .

You want to fence in a rectangular area for a dog run along the back of your home. Your home will serve as one side of the run, so you only need to purchase fencing material for the remaining three sides. The fencing material costs $1.50 per foot, and you have a budget of $90.00. How many square feet are in the largest dog run you can afford to build?

Is the function quadratic? If so, write the function in the form .

Which of the following quadratic functions have zeros at x = -5 and x = 2?

A projectile's height Above ground is a quadratic function of time t in seconds since launched. Three values of the function are given in the table below. What is the practical interpretation of?

If is quadratic, then it can be written as . If is not quadratic, enter "DNE" for each of the blanks.

The graph of has vertex ( _____, _____ ) and axis of symmetry x = _____.

Find a formula for the parabola:

Find the zeros of by factoring. List the answers in the form "A, B", with A < B.

Find a formula for the quadratic function which has only one zero at and contains the point

The following figure gives the graph of , a quadratic function with vertex (6, 4). The formula for is , where a = _____, b = _____, and c = _____.

A projectile's height above ground in feet is a quadratic function of time t in seconds since launched. Three values of the function are given in the table below. What is the maximum number of feet above the ground that the projectile reaches?

Suppose What is ?

The height of a baseball in feet seconds after it has been hit is given by . At what time does the baseball reach maximum height? Give your answer correct to 3 decimal places.