Question

help

Answer 1

@sailor

Answer 2

@dontsaymyname

Answer 3

@laylalyssa

Answer 4

🧀

Answer 5

To write a rule for the transformation described, we can break it down into two parts:

1. Translation 1 unit left and 6 units down: This can be represented as g₁(x) = (x - 1, f(x) - 6).
2. Vertical shrink by a factor of 1/2: This can be represented as g₂(x) = (x, 1/2 * f(x)).

Combining these two transformations, the rule for g is:
g(x) = g₂(g₁(x)) = (x - 1, 1/2 * (f(x) - 6))

Now, let's identify the vertex of the transformed graph:

The original function f(x) = 3(x + 2)² is in the form f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

Comparing this with the equation of our transformed graph, we see that the vertex of the transformed graph is obtained by applying the translation and shrinkage to the vertex of the original graph.

So, the vertex of the transformed graph can be found by substituting x = -2 (the x-coordinate of the original vertex) into the rule of g:
g(-2) = (-2 - 1, 1/2 * (f(-2) - 6))
= (-3, 1/2 * (3(-2 + 2)² - 6))
= (-3, 1/2 * (3(0) - 6))
= (-3, 1/2 * (-6))
= (-3, -3)

Therefore, the vertex of the transformed graph is (-3, -3).

Answer 6

Hope this helps

Answer 7

Your greatly welcome

Answer 8

I don't know what i'm typing in wrong