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14 June, 23:34

A parabola has a line of symmetry x = - 5. The minimum value of the quadratic function that it represents is - 7. Find a possible equation of this parabola and explain how you found it.

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  1. 14 June, 23:38
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    The standard equation of a parabola is:

    (y-k) = a (x - h) ², where h and k are the coordinates of the Vertex

    Since the vertex is ( - 5, - 7), then:

    (y + 7) = a (x + 5) ².

    It's given that the vertex is a minimum, that means the coefficient a>0 and the parabola is open upward.

    Depending on the value of a (always a>0), the equation:

    y = a (x-5) ² + 7 is a parabola
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