Question

Question 1 This question has two parts. First, answer Part A. Then, answer Part B.

Part A
Describe how the graph of g(x) = - 1/2 * (x + 4) ^ 2 - 1 is related to the graph of the parent function

The graph of f(x) = x ^ 2 is reflected across the ___ and___ vertically. The graph translated 4 units ___ and 1 unit ___

Part B Select the correct graph of g(x) = - 1/3 * (x + 4) ^ 2 - 1

Answer 1

Check the picture below on the left-hand-side, that's just a transformations template, so hmmm let's use that to rewrite g(x)

`g(x)=\stackrel{A}{-(1)/(3)}(\stackrel{B}{1}x\stackrel{C}{+4})^2 \stackrel{D}{-1} \\\\[-0.35em] ~\dotfill\\\\ A=-\cfrac{1}{3}\qquad \textit{flipped upside-down and stretched by a factor of 3}\\\\ B=1\qquad C=+4\qquad \textit{horizontal shift of }(4)/(1)\textit{ to the left}\\\\ D=-1\qquad \textit{vertical shift downwards of 1 unit}`

Check the picture below on the right-hand-side.

Answer 2

The graph of f(x) = x ^ 2 is reflected across the y-axis and reduced or shrunk by 1/3 vertically. The graph translated 4 units to the left and 1 unit Down

Explanation:

The graph of f(x) = x ^ 2 is reflected across the y-axis and reduced or shrunk by 1/3 vertically. The graph translated 4 units to the left and 1 unit Down.

Y axis because it's multiplied by -1/3 which is negative

Reduced or shrunk by 1/3 because 1/3 is a fraction

4 units to the left because (x+4) What x=0 could do now the x=-4 can do so the graph shifted to the left

And 1 unit down because of the -1 at the end.