Question

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (6, -3). What is the vertex of the function defined as
g(x) = f(-x) - 3?

Answer 1

Answer: (-6, - 6)

Step-by-step explanation:

Here we have two transformations, and the first step will be to explain those transformations:

Reflection over the y-axis.

For a function f(x), the reflection over the y-axis is written as:

g(x) = f(-x)

Then if we initially had a point (x, y), the transformed point will be (-x, y).

Vertical translation.

We can define a vertical translation of N units as:

g(x) = f(x) + N

if N > 0, the translation is up.

If N < 0, the translation is down.

Then if we start with a point (x, y), the transformed point will be (x, y + N)

In the case of this problem we have g(x) = f(-x) - 3

This means that N = -3

Then if we initially had the vertex at the point (6, - 3)

The transformed point will be: changing the sign of the x-component and subtracting 3 in the y-component, then the transformed vertex point is:

(-6, -3 - 3) = (-6, - 6)

Answer 2

The vertex of the resulting  parabola will be (-6, -6)

Rule of reflection

Given the function y= f(x), plotted on a graph and the vertex of the resulting

parabola is (6, -3), if this coordinate is reflected over the y-axis, the reflection rule will be:

• $(x,y) \rightarrow (-x, y)$

• The coordinate (6, -3) under this translation will give (-6, -3)

To get the corresponding function $g(x) = f(x) - 3$

$g(x) = [(-6, -3) - 3]\\g(x) = (-6, -3-3)\\g(x) =(-6, -6)$

Hence the vertex of the resulting  parabola will be (-6, -6)

Learn more on reflection here: https://brainly.com/question/14460986