Exam 8: Quadratics and the Mathematics of Motion

Find the quadratic function with x-intercepts -5 and -2 and y-intercept 30. Write your answer in standard form .

A free falling body has an initial velocity of 16 m/sec. Find the equation to describe the distance traveled in t seconds. Assume that g = 9.8 m/sec².

An object that is moving horizontally along the ground is observed to have an initial velocity of 92.8 m/sec and to be accelerating at a constant rate of 11 m/sec². Determine the average velocity between 3 and 5 seconds.

Find a quadratic function, , that has vertex and . Write your answer in standard form .

Find the average rate of change of the function

Convert the function into standard form,

Select the equation whose graph is the graph of shifted 5 units up.

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

Find two different equations; one where a = 4 and one where a = 5; for a parabola that goes through the points (1, 1) and (9, 1). Write the function in form.

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

Select the equation that best describes the graph.

For the quadratic function pictured determine whether the parabola is concave up or concave down.

Using the height equation , find the height, in ft, at t = 3 seconds.

Which of the following is the graph of the average rate of change of the quadratic function .

At t = 0, a ball is thrown upward at a velocity of 49 m/sec. The ball's height is measured in meters above the ground. Assuming the height at t = 0 is 0 m, what is the height at t = 2?

Using the equation , fill in the table.

Find coordinates of the focus of the parabola given by the equation

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

The equation d = 490t² + 10t describes the relationship between distance fallen, d, in cm, and time, t, in seconds, for a free falling object. What is the initial velocity of the object?

The light source is placed at the focus of a parabolic reflector. If the light source is 12.5 inches away from the reflector which is 2.88 inches deep, how many inches wide does the reflector need to be? Round your answer to 2 decimal places, if necessary.