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# Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1, and passes through the point (9, -1). Write the equation of the parabola in vertex form.

**Solution:**

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part.

Given an __axis of symmetry__ at x = 8, a maximum height of 1, the point (9, -1).

Standard form:

(x - h)^{2}= 4p(y - k), (h, k) = (x, y) __coordinates__ of the vertex

Considering given __parabola__:

vertex: (8, 1)

(x - 8)² = 4p(y - 1)

Let us solve for 4p by using the coordinates of the given point (9, -1)

(9 - 8) = 4p(-1 - 1)

1 = 4p(-2)

4p = -1/2

Equation of given parabola: (x - 8)² = -(y - 1)/2

## Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1, and passes through the point (9, -1). Write the equation of the parabola in vertex form.

**Summary:**

Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1, and passes through the point (9, -1). The equation of the parabola in vertex form is (x - 8)² = -(y - 1)/2 .

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