A parabola is represented by the equation...?

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  • 4 weeks ago

    We can complete the square and get:

    y = x² + 4x + 4 - 4

    y = (x + 2)(x + 2) - 4

    y = (x + 2)² - 4

    That's in vertex form of a parabola:

    y = a(x - h)² + k

    In your case:

    a = 1

    h = -2

    k = -4

    Since 'a' is positive, you have an upward facing parabola where the vertex is therefore a minimum. The coordinate of the vertex is (-2, -4).

    The line of symmetry goes through that vertex, so is x = -2.

    Answer:

    A. The parabola has a minimum at (-2, -4)

    C. The parabola has an axis of symmetry of x = -2

    The other statements don't apply to this parabola.

  • 4 weeks ago

     A parabola is represented by the equation y = x^2 + 4x. 

     Which of the following is true about the parabola?

     A. The parabola has a minimum at (-2, -4). ✔

     B. The parabola has an axis of symmetry of x = 2.

     C. The parabola has an axis of symmetry at x = -2. ✔

     D.  The parabola has a maximum at (2, 4).

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