Exam 8: Quadratics and the Mathematics of Motion

A projectile is at a height centimeters at time t = 0 seconds. Find the height at time t = 5 sec.

A projectile is at a height feet at time t = 0 seconds. At what time does the projectile reach the ground?

Find the focus of a parabola represented by the equation with vertex at (-1, -4).

Find values for A and B using what you know about completing the square.

Find the vertex of the parabola

Find the coordinates of the vertex of the parabola given by . Give your answer as a reduced fraction or whole number.

The equation d = 16t² + 12t describes the relationship between distance fallen, d, in ft, and time, t, in seconds, for a free falling object. What is the acceleration of gravity on the object?

Select the choice which best describes the graph of .

Transform the function into a new function by compressing by a factor of 0.2, reflecting across the x-axis, and then shifting the result down 3 units. Find the equation of

The antenna is placed at the focus of a satellite dish. If the satellite has a 6-inch diameter and is 0.54 inches deep, how many inches from the vertex of the satellite dish should the antenna be placed? Round your answer to 2 decimal places, if necessary.

For the quadratic function pictured determine the equation of the axis of symmetry.

Find any solutions to the equation Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Find the x-coordinate of the vertex of the parabola given by . Give your answer as a reduced fraction or whole number.

A rancher has 2,800 feet of fencing. He wants to use all 2,800 feet to construct a rectangle with 2 interior separators that together form 3 rectangular pens. What are the dimension of the larger rectangle that give the maximum area? (Give both the length (L) and width (W).)

The equation d = 490t² + 26t describes the relationship between distance fallen, d, in cm, and time, t, in seconds, for a free falling object. What is the distance fallen by the object at time t = 6 sec?

Write the function in factored form, . Write the values for r₁ and r₂ in ascending order (r₁2.) For complex answers enter .

A free falling body has an initial velocity of 926 cm/sec. Find the velocity of the object at time t = 5 seconds. Assume that g = 980 cm/sec².

After 2 seconds, a falling object has a velocity of 26.6 m/sec. Find the velocity of the object at time t = 8 seconds. Assume that g = 9.8 m/sec².

Find the average rate of change of the function over the interval

Find values for A and B using what you know about completing the square. \