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Factoring and Graphing Equations

Please help me solve the problems in the attached practice work.

1) Solve the following by factoring:

a) 5t^2 - 10t = 0
b) x^2 - 3x - 10 = 0

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

a) f(-2)
b) f(4)

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.

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.
b) Does this function have a maximum or a minimum?
c) What is the equation of the line of symmetry for this graph?
d) What are the coordinates of the vertex in (x, y) form?

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

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

x y
-4
-3
-2
-1
0
1
2

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 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.
b) How high is the rock after 2 seconds?
c) After how many seconds will the graph reach maximum height? Show your work algebraically.
d) What is the maximum height?

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Solution Summary

A complete, neat and step-by-step solution is provided in the attached file, covering how to solve all the problems by factoring and quadratic formula.

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