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Math 110 Name: ______________________________

Exam III: Chapter 4, Sections 5.0 and 5.1, and Exam II Date: ______________________________

Directions: Show all work to get full credit.

1. Simplify the following expressions. Do not use decimals.

a. b.

2. Factor the expression completely:

3. Solve the quadratic equation using the factoring method:

4. Find the quadratic equation given the points (-4, 0), (-3, 16), and (5, 0) are on the parabola.

5. Given the quadratic equation , complete parts ‘a’ – c’ below:

a. x-intercept(s): __________________

b. y-intercept: __________________

c. shift: __________________

6. Convert 60 miles per hour into a number of feet per second using the unit analysis procedure.

Given: 5280 feet = 1 mile

1 hour = 60 min

1 minute = 60 sec

7. Inspect the overlapping triangles. Set up and solve a proportion to find the missing side x.

8. Find the quadratic equation for the parabola below. Assume the ‘a’ value is 1.

Note: Pay attention to the scaling.

Equation: _________________________

9. Use the function y = x² + 2x – 3 for ALL parts ‘a’ – ‘e’ below:

a. Convert the equation to vertex form using the completing the square procedure.

b. Use the standard form and/or the vertex form from above to identify the following features of the graph:

The width as compared to y = x² (choices: same, more narrow, wider) _____________________

The way the parabola opens (up or down) ____________________

The coordinates of the y-intercept point ____________________

The vertex point ______________________

The axis-of-symmetry equation _____________________

c. Find the value of the discriminant and state what this value tells you about the x-intercepts of the graph of y = x² + 2x – 3.

d. Solve for the x-intercept(s), if they exist, using any symbolic method of your choice.

e. Use the information from above to give a detailed sketch of the parabola. Label all of the main features: x-intercepts (if any), y-intercept, vertex, axis-of-symmetry. Use graph paper.

10. Solve using any symbolic method of your choice:

11. For both parts ‘a’ and ‘b’ below, give a sketch of each parabola with the given quadratic

equation.

Note: The graph of is on each grid below so you can use it as a reference graph. You just

need to graph the new function.

a) b)

Part II: Graphing calculators allowed.

12. A happy San Diego Charger fan throws a football vertically into the air with an initial velocity of 15 ft/sec. Assume the ball leaves the fan’s hand at a height of 6.5 ft. Let g = 32.2 ft/sec².

a. Write the simplified equation representing the height the football is off the ground as a function of

time. Use the vertical motion formula:

b. How long does it take for the football to fall to 3 feet off the ground?

Note: Any solving approach is acceptable. Round answer to the hundredths place.

c. What is the maximum height the football is from the ground? When does this occur?