Question

Post test comic sections

Answer 1

The focus point of the parabola is (2, 0), which corresponds to option D.

The given equation of the parabola is in the form
`\(y = a(x - h)^2 + k\)`, where (h, k) is the vertex of the parabola. The focus point of a parabola is given by
`\((h, k + (1)/(4a))\)`.

In the equation
`\(y = (1)/(8)(x^2 - 4x - 12)\)`, we can rewrite it in the form
`\(y = a(x - h)^2 + k\):`

`\[ y = (1)/(8)(x^2 - 4x - 12) \]`

`\[ y = (1)/(8)(x^2 - 4x + 4 - 4 - 12) \]`

`\[ y = (1)/(8)((x - 2)^2 - 16) \]`

`\[ y = (1)/(8)(x - 2)^2 - 2 \]`

Now, we can see that the vertex (h, k) is (2, -2). The focus point is then given by
`\((h, k + (1)/(4a))\)`.

For this parabola,
`\(a = (1)/(8)\)`, so the focus point is:

`\[ (2, -2 + (1)/(4((1)/(8)))) \]`

`\[ (2, -2 + (1)/(4((1)/(8)))) \]`

`\[ (2, -2 + 2) \]`

`\[ (2, 0) \]`

Therefore, the correct focus point is (2, 0).