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    quadratic equation and inequality

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    1) What is the meaning and purpose of the axis of a quadratic function?

    2) Solve the inequalities. State the solution set using interval notation for:
    (x - 4) / (x + 3) < 0
    and then for:
    (x - 4) / (x + 3) > 0

    What do you get when uniting the two sets of solutions?

    3) The surface area A, of a cylinder with height h, and radius r, is given by the equation A = 2prh + 2pr^2. Find the radius of a cylinder with height 2 cm and area 4p cm2.

    4) An arrow is shot straight upward with a velocity of 96 feet per second at instant t0 = 0; its altitude is defined in time by the following function:
    f(t) = -16t² + 96t + 6.
    From what altitude is it shot? For how many seconds is this arrow more than 86 feet high?

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    https://brainmass.com/math/basic-algebra/quadratic-equation-inequality-108140

    Solution Preview

    Please see the attached file for detailed solutions.

    ) What is the meaning and purpose of the axis of a quadratic function?
    For a quadratic function of , it can also be written as

    Then line of axis is , this is also the symmetric line of the graph of this quadratic function.
    When you graph the curve, you can just draw the left or right side of the , then the other half can be obtained by the symmetry.

    Another use of axis of the quadratic function is the ...

    Solution Summary

    The solution explains the meaning of the line of axis of a quadratic equation. It also explains how to solve a complex inequality. Finally, it finds the height of the arrow when it is shot straight upward.

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