Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7, 1) . write the equation of the parabola in vertex form. explain how it is solved.

The vertex-form of the equation of a parabola is , 
where (h, k) is the vertex point.

We are given that 9 is the maximum point, and that the axis of symmetry is the line x=-5.

The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5. The maximum height is 9 means that the y-coordinate of the vertex is 9.

So: (h,  k)=(-5, 9).

Substituting in the vertex-form, now we have:

.

We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation. That is:



Now we have all the constants h, k and a, so we are able to write the equation:

.

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