In Exercises 53-66, begin by graphing the standard quadratic func...

Question

In Exercises 53-66, begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. h(x) = (1/2) (x − 1)² – 1

Accepted Answer

Use the graph of the function F of X equals X to the third or applying the transformation of graphs to graph the function according to the given condition G of X equals one third multiplied by X minus two to the third plus two. Now, to solve this, we need to determine our transformations going from F of X to G FX or ethics. Is it the third G FX one third multiplied by X minus two to the third plus two. Now we first notice we have a one third in front of our variable X that implies we have a vertical shrink because our number one third is between zero and one. You will call that a vertical shrink. We also have horizontal and vertical shifts. We notice we have a two inside of the parentheses with our X and we're subtracting it. That means we are shifting to the right. Bye too. In addition, we have a upward shift because of our plus two on the outside, we're shifting up by two as a result. Now we need to find a graph going from X to the third to our new graph G of X. That follows each of these transformations. If you look at our possible graphs, we can determine graph C will follow all of our transformations. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 53-66, begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. h(x) = (1/2) (x − 1)² – 1