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 .