algebra 2

a quadratic equation can be written in vertex form or in standard form. sometimes one form is more beneficial than the other. identify which form would be more helpful if you needed to do each task listed below and explain why.
a. factor the equation.
b. graph the parabola
c. identify the vertex, minimum, or maximum of the parabola.
d. solve the equation using the quadratic formula.

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  1. a) clearly in standard form
    b) I find the vertex form useful, since you immediately have one point and the axis of symmetry. All you need is another point and its reflection in the axis of symmetry and you should be able to sketch the graph
    c) If you have to find the vertex, max/mins etc, what form contains the word vertex ??
    d) The formula is defined according to a, b, and c of
    ax^2 + bx + c = 0 . So what do you think?

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    Reiny
  2. below are suppose the be the questions:

    a. factor the equation
    b. graph the parabola
    c. identify the vertex minimum or maximum of the parabola
    d. solve the equation using the quadratic formula

    below are the answers:

    Vertex form is most helpful for all of these tasks.
    Let
    .. f(x) = a(x -h) +k ... the function written in vertex form.

    a) Factor:
    .. (x -h +√(-k/a)) * (x -h -√(-k/a))

    b) Graph:
    .. It is a graph of y=x^2 with the vertex translated to (h, k) and vertically stretched by a factor of "a".

    c) Vertex and Extreme:
    .. The vertex is (h, k). It is a maximum if "a" is negative; a minimum otherwise.

    d) Solutions:
    .. The quadratic formula is based on the notion of completing the square. In vertex form, the square is already completed, so the roots are
    .. x = h ± √(-k/a)

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