algebra

Identify the vertex and axis of symetry of the parabola. Identify points corresponding to P and Q. on the graph it has P at (-2,4) and a point at Q at (-1,7). my teacher says the answers were the vertex was (-1,3) the Axis of symmtry was X=-1 the P is (0,4) and Q is (-3,7).. how do you figure out each of those steps? im confused with how to do the whole problem

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  1. The P and Q coordinates in your first statement do not agree with the P and Q in your last statement. I would need to see the graph to know what this problem is all about.

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  2. I will try to reverse engineer this mess.
    (y-3) = k (x+1)^2
    if the vertex is at (-1,3) and x=-1 is the axis

    put in P at (-1,7) impossible because y = 3 when x = -1

    so I will try the second pair of points

    P at (0,4)
    (4-3) = k (1)^2
    so k = 1
    so
    y - 3 = (x+1)^2
    try Q at (-3,7)
    4 = (-2)^2
    YES
    so the parabola with axis of symmetry at x = -1 and vertex at (-1,3) can contain the SECOND pair of points P and Q
    rewrite in standard form
    y = 3 +x^2 + 2 x + 1
    y = x^2 + 2 x + 4

    I have no idea what the two original points P and Q were. They are on some other curve.

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