Question

X = -6(y - 8)⁻³. Vertex =
a) (8, 0)
b) (-6, 8)
c) (0, 8)
d) (0, -6)

Answer 1

The vertex of the quadratic function
`\(X = -6(y - 8)^(-3)\)` is (0, 8). Thus, the correct option is a.(8, 0).

Step-by-step explanation:

To find the vertex of the given quadratic function, it is helpful to rewrite the equation in a standard form
`\(y = a(x - h)^2 + k\),` where (h, k) represents the vertex. In this case, we have
`\(X = -6(y - 8)^(-3)\).` To put it in the standard form, we can take the reciprocal of both sides and rearrange:
`\((1)/(X) = -6(y - 8)^(3)\).`

Now, comparing this with the standard form, we can identify that the vertex is at (0, 8), where
`\(h = 0\)` and
`\(k = 8\).` Therefore, the correct option is (c) (0, 8).

Understanding the structure of quadratic functions allows us to recognize the vertex form and easily identify the coordinates of the vertex. The vertex form
`\(y = a(x - h)^2 + k\)`provides valuable insights into the shape and direction of the parabola. In this case, the function is inversely proportional to
`\(y\),` indicating that it will be reflected over the x-axis. The presence of
`\((y - 8)^(-3)\)` implies that the vertex is located at (0, 8), making option (c) the correct choice. Thus, the correct option is a.(8, 0).