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    Quadratic Equations - MTH133

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    1) Solve the following by factoring; find the solutions, factoring alone is not the objective of the problems:

    a)

    Answer:
    Show your work here:

    b)

    Answer:
    Show your work here:

    2) If , find:

    a) f(2)

    Answer:
    Show your work here:

    b) f(-3)

    Answer:
    Show your work here:

    3) Solve using the quadratic formula.

    Answer:
    Show your work here:

    4) Use the graph of to answer the following:

    a) Without solving the equation, or factoring, determine the solution(s) to the equation using only the graph.

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

    b) Which does this function have, a maximum or a minimum?

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

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

    Answer:

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

    Answer:

    5) a) Calculate the value of the discriminant of .

    Answer:
    Show your work here:

    b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?

    Answer:

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

    Answer (fill in y column)
    x y
    -2
    -1
    0
    1
    2
    3

    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 sketch the graph. Read the information in the assignments 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.

    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
    Answer:

    b) How high is the rock after 1 second?
    Answer:
    Show your work here:

    c) After how many seconds will the graph reach maximum height?
    Answer:
    Show your work here:

    d) What is the maximum height?
    Answer:
    Show your work here:

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    https://brainmass.com/math/basic-algebra/quadratic-equations-mth133-229882

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