Consider the following nonlinear system. Work Exercises 75 –80 in...

Question

Consider the following nonlinear system. Work Exercises 75 –80 in order.
y = | x - 1 |
y = x^2 - 4

How is the graph of y = x^2 - 4 obtained by transforming the graph of y = x^2?

Accepted Answer

Hello everybody. I hope you're doing. All right. Today, today we're going to be looking at this math question that states describe the transformation required to draw the graph of Y equals X squared minus six from the graph of Y equals X squared. Now, the s provided are a shift, a graph of Y equals X squared six units up B shift A graph of Y equals X squared six units down C shift A graph of Y equal X squared six units to the left or D shift A graph of Y equals X squared six units to the right. Now, when looking at this question, we have to focus on the equation, they give us so they give us Y equals X squared minus six. And we have to think about different rules that we know for different transformations of graphs. In this case, I know that this format matches a vertical transformation that can be, is usually generally written as Y equals F of X plus K. So this format matches the formula that we have. And with this vertical transformation format, the rule states that if K it's greater than zero, move the graph moves up. And if K is less than zero, the graph moves down. So let's compare this to what we have in this case, six is equal to K and, and or, or in our case, if we have a minus six, so it would be negative six and negative six is less than zero. Therefore, it shifts down. So our graph of Y equals X squared would be shifting six units downwards six units down. So that is the transform. The only transformation here because we are, we have Y equal X squared. And the only other thing that we have in the equation is the minus six. So the only transformation here will be six units down or in this question answer choice B So I hope that was helpful. And until next time.

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Consider the following nonlinear system. Work Exercises 75 –80 in order. y = | x - 1 | y = x^2 - 4 How is the graph of y = x^2 - 4 obtained by transforming the graph of y = x^2?