Question

Does anyone know the answer to this?

Answer 1

`g(x) = 3(x - 12)^(2) - 5`

Explanation:

Horizontal translations = f(x ± h)

Reflection over the x-axis = - f(x)

For the function
`f(x) = - 3(x - 4)^(2) +5`, translating the parabola 8 units to the right means the horizontal shift of the graph, adding (- 8) to the h input. This is represented by:
`g(x) = - 3(x - 12)^(2) +5`.

Next, flipping the graph over the x-axis represent a reflection. Since we currently have a negative coefficient for the value of a, then the opposite of a negative coefficient is a positive coefficient.

Therefore, the rightward horizontal translation of 8 units, and the reflection of the graph over the x-axis is represented by:

`g(x) = 3(x - 12)^(2) - 5`

For your reference, the three images below shows the transformations on the graph. The first image is the original function (in red parabola). The second image represents the reflection over the x-axis (green parabola). The third image shows the horizontal shift, 8 units to the right (blue parabola). If you take note of the varying values in vertices, (h, k ) for the three graphs, you'll see that the original vertex was (4, 5) and the new vertices for the transformations are (4, -5) for the reflection and (12, -5) for the shift.