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# multiple algebra problems

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1a) Solve the following quadratic equation by factoring:
Show work here:
symbols, such as the square root.
Show work here:
1c) Compute the discriminant of the quadratic equation 10 .
Then write a brief sentence describing the number and type of solutions for the
equation.
Show work here:
2) Use the graph of 4 5 2 y ? ?x ? x ? to answer the following:
a) Without solving the equation, or factoring, determine the solution(s) to the
equation 4 5 0 2 ? x ? x ? ? using only the graph.
Explain how you obtain your answer(s) by looking at the graph in a brief sentence:
b) Does this function have a maximum or a minimum?
Explain how you obtain your answer by looking at the graph in a brief sentence:
c) What are the coordinates of the vertex in (x, y) form?
d) What is the equation of the axis of symmetry for this graph?
3) The path of a falling object is given by the function 0 0
2 s ? ?16t ? v t ? s where
0 v represents the initial velocity in ft/sec and 0 s represents the initial height in feet.
a) If a rock is thrown upward with an initial velocity of 64 feet per second from the top of
a 25-foot building, write the height (s) equation using this information.
Typing hint: Type t-squared as t^2
b) How high is the rock after 1 second?
c) After how many seconds will the rock reach its maximum height?
d) What is the maximum height?
4a) Find the corresponding y values when x = -2, -1, 0, 1, 2, 3 for the equation,
2 2 y ? x ? x ? .
x y
-2
-1
0
1
2
3
Show your work here: (type x-squared as x^2)
b) Use Microsoft Excel or another web-based graphing utility to plot the points found in part a) to sketch the graph here. Read the information in the assignments list to learn more about how to graph in MS Excel.
c) Determine the two x-intercepts and the vertex of this parabola in (x, y) form and explain how you found these ordered pairs in a sentence. Answers: