# Unit 2 Individual Project of course MTH 133

Please see the attached file for the fully formatted problems.

MTH133

Unit 2 Individual Project

Name:

Typing hint: Type x2 as x^2 (shift 6 on the keyboard will give ^)

1) Solve the following by factoring:

a) 5t^2 - 10t = 0

Answer:

Show your work here:

b) x^2 - 3x - 10 = 0

Answer:

Show your work here:

2) If f(x) = 3x^2 + 5x - 2 , find:

a) f(-2)

Answer:

Show your work here:

b) f(4)

Answer:

Show your work here:

3) Solve 3x^2 + 19x - 14 = 0 using the quadratic formula. Read the information in the assignment list to learn more about how to type math symbols in MS Word.

Answer:

Show your work here:

4) Use the graph of y = x^2 - 2x - 8 to answer the following:

a) Without solving the equation (or factoring), determine the solutions to the equation x^2 - 2x - 8 = 0 by inspecting the graph.

Answer:

Explain how you obtain your answer(s) by looking at the graph:

b) Does this function have a maximum or a minimum?

Answer:

Explain how you obtain your answer by looking at the graph:

c) What is the equation of the line of symmetry for this graph?

Answer:

d) What are the coordinates of the vertex in (x, y) form?

Answer:

5) a) Calculate the value of the discriminant of x^2 + 2x + 1 = 0 .

Answer:

Show your work here:

b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y = x^2 + 2x + 1 have? Why?

Answer:

6) a) Find the corresponding y values for x= -4, -3, -2, -1, 0, 1, 2, if y = x^2 + 2x - 15 .

Answer (fill in y column)

x y

-4

-3

-2

-1

0

1

2

Show your work here: (type x-squared as x^2 unless using a superscript feature).

b) Use Microsoft Excel or another web-based graphing utility to plot the points found in part a) and to draw the graph. Copy and paste the graph here. Read the information in the assignment list to learn more about how to graph in MS Excel.

7) The path of a falling object is given by the function s = -16t^2 +v0t + s0 where represents the initial velocity in ft/sec and represents the initial height in feet. Also, s represents the height in feet of the object at any time, t, which is measured in seconds.

a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.

Typing hint: Type t-squared as t^2

Answer:

b) How high is the rock after 2 seconds?

Answer:

Show your work here:

c) After how many seconds will the graph reach maximum height? Show your work algebraically.

Answer:

Show your work here:

d) What is the maximum height?

Answer:

Show your work here:

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