For each equation, (a) give a table with at least three ordered p...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=x^2

Accepted Answer

Hello everybody. And I today today we're going to begin this question that states for the following equation identify three ordered pairs and show that the graph passes through these points where our equation is Y equals three X squared. Now the answer choices provided all show different types of graphs. Answer choice A shows a parabola with points at negative 12 comma 16 3 comma one and nine comma nine answer choice B shows a parameter with points at negative six comma negative three comma three and three comma three as trace C shows a Parabola with points at negative three, comma 27 1, comma three and two comma 12. And a choice D shows a parabola with points at negative two comma four three comma nine and a point at the origin which is the vertex. Now, for this question, we have to ask ourselves, what is our graph going to look like? So we know that three X squared, the parent function of that will be Y equals X squared. And this means with the three in front multiplying the X squared, that just means there's going to be a transformation. So the X squared value will have different answers with the three in front. However, the same general shape will take place, which will be a problem. So our parent function is a problem. So now we just have to see what the different values look like with the three in front. And to do that, we just do a T chart where we have an X column on the left and A Y column on the right. And I'll test different points. So I'll test every X from negative three to positive three, every whole value. So I have negative three, negative two, negative 1012 and three as XS that will be tested. Now, all I have to do is plug in the negative 34 R Y equals to X squared. So I'll show you, for example, if, if we have negative three will have Y equals three multiplying a negative three squared which will be three, multiplying negative three squared is positive nine. So we'll have three times three, multiplying a positive nine, which is 27. So when we have an X of negative three, we have a Y of 27. Now because it's a parabola, we know that every value that we get for a positive X will be reflected and be the same value for that same positive Y or er X. So if we have a negative X, let's say a negative three gives us a Y of 27. That's same X but positive. So a positive three will give us the same Y 27. So we can plug that in as well. Now, we can plug in negative two and we do the same thing as we do with negative three. So we do that and we plug in the negative two, we'll get a Y of 12 and we can put the same Y for the positive two because once again, it's reflected, if we have plug in the X of negative one, we'll get a Y of three and we can be reflected and put that in for the positive one as well. And for an X of zero, we get a Y of zero or the origin. So that means we have points negative three comma negative two comma 12 negative one, comma three zero, comma zero one comma three two comma 12 and three comma 27. So now we just look at the different graphs that they provided us. First, we look at answer choice A, we see that they have a, the, the vertex is not the origin, which is what we have. And we see that they have a point at an X of three, they have it at three comma one. However, for us, we have a point where we have an X of three, we have three comma 27. So a answer choice A can be eliminated. Now we move on to answer choice B they once again, have a vertex of the origin, which is what we have for an X of three, they have three comma three. So that doesn't match. And for their X of negative three, they also have negative three comma three, which also doesn't match. So we can eliminate as choice B now we move on to answer tray C they once again have a parabola with a vertex at the origin which matches with what we have at an X of one. They have one comma three which matches at an X of two. They have two comma 12 which also matches and at an X of negative three, they have negative three comma 27 which also matches with our answers and leads us to pick answer choice C as our answer, a Parabola with a vertex at the origin with points at two comma 12, 1 comma three and negative three comma 27. So I hope that was helpful. And until next time.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=x^2

Key Concepts

Ordered Pairs

Graphing Quadratic Functions

Function Evaluation

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