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find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y=-2x^2-8x+3. explain the steps please. :)

  • algebra -

    The axis of symmetry of a parabola of the form y=ax²+bx+c is always vertical.

    If a > 0, the parabola is concave upwards, and if a<0, the parabola is concave downwards.

    The vertex of a parabola can be obtained by completing the squares, namely
    or at
    x= -b/2a, at which point
    Thus the vertex of the parabola
    y=ax²+bx+c is at
    (-b/2a, c-b²/4a)
    The vertical axis of symmetry passes through the vertex, thus has the equation:

    Apply the above the equation to the given problem and post the answer for verification if required.

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