Explore BrainMass
Share

Explore BrainMass

    Graphing Functions: Completing the Square, Quadratic Functions, Axis of Symmetry, and Intercepts

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    1. Using completing the square to describe the graph of the following function. Support your answer graphically.
    f(x) = -2x^2 + 4x + 1
    2. Graph the function: g(x) = (x-2)^3
    3. Determine the quadratic function f whose vertex is (3, -2) and passes through (2, 1)
    4. Graph the line containing the point P and having slope m: P = (2, -7); m = 0
    5. Graph the function and state the vertex, the axis of symmetry, the intercepts, if any: f(x) = x^2-6x+5
    What is the vertex?
    What is the axis of symmetry?
    What are the intercepts, if any?

    © BrainMass Inc. brainmass.com October 10, 2019, 6:25 am ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/completing-square-quadratic-functions-axis-symmetry-543240

    Solution Preview

    1.

    This parabola has a vertex at

    We see that as the function approaches , so the vertex point is a maxima (the parabola opens down).
    The parabola intersects the x-axis when


    Which gives:

    It intersects the y-axis when x=0 and this gives:

    To summarize:
    The parabola has a vertex which is a maxima at so its symmetry axis is x=1
    It intersects the x-axis at and
    It intersects the y-axis at ...

    Solution Summary

    The solution assists with completing the square, quadratic functions, axis of symmetry and intercepts. The axis of symmetry and intercepts are analyzed.

    $2.19