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) = -2(x+2)²+1

Accepted Answer

Use the graph of the function F of X equals X to the third for applying transformation of graphs to graph the function according to the given condition G of X equals negative five multiplied by X minus one to the third minus two. Now, to graph this, we need to determine the transformations of our graph. We have G M X equals an A to five multiplied by X minus one to third minus two. Now we can see a few transformations right off the bat. We first have a negative five in front of our X minus one to the third. This implies we have a vertical stretch and we will have vertical stretch of five. Now the negative in front of the five tells us we will flip our equation over the X axis. Next, we look at our shift, we have a negative one inside the parentheses with the X. This means we will shift horizontally to the right by one. Finally, we have a negative two on the outside which means we shift downwards, bye too. So we need the graph that has been stretched by five flipped over the X axis shifted to the right by one and shifted down by two. Now, on the original alpha X function, we have a point at 00. If we're to transpose this, the G FX, we have a point that shifted to the right by one and down by two, we then have a point at one negative two. If you look down, we noticed the only graph that has a point at one negative two is graph D 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) = -2(x+2)²+1

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