Graph each function. See Examples 1 and 2. ƒ(x)=-(1/2)x^2

Question

Accepted Answer

Hello everybody. I hope you're doing. All right. Today today we're gonna be looking at this math question that says for the following function sketch its graph where the function is H of X is equal to negative 1/5 multiplied by X squared. And the extras provided are four different graphs with answer choice A being a parabola opening upwards with points at negative 15 comma 45 negative five comma five and 10 comma 20. And then in a vertex at the origin zero comma zero S trace B has points at negative 15 comma negative 45 negative five comma negative 5 10 comma negative 20. And in origin at zero comma zero. S choice C has points at negative one comma five N two comma and in origin at zero comma zero and S choice D has points at negative one comma negative five two comma negative and in origin at zero comma zero. Now, the first thing we gotta think about is what is this graph going to look like? Even though we have a negative 1/5 multiplying the X squared, this will ultimately look like or have at least the same general shape as the graph of a parabola. So that would be X squared by itself has a graph of, let's say a regular, regular parameter like this. That's what a graph of a regular parameter would look like. However, if you do negative X squared, you would now be flipping it. So instead of opening upwards, you're opening downwards. Now, what do we have in this case? Well, we have a positive X squared but we're multiplying it by a negative value in front, negative 1/5. So even though the X squared will be positive, once you multiply it by the negative, it will turn negative. So we will have a negative X squared at the end. So we'll have a graph opening downwards. So right away, we can eliminate answer choices C and answer choice A because they have their parabola opening upwards. Now, how do we decide between choice B and D? Well, we can do some plugging of points and see what we obtain. We see that in choice B, they reach A Y value of negative five when their X is negative five. And in D they reach the Y value of negative five when the X is negative one. So we just have to plug in one of those XS and see which one gives us that Y value, which one would be correct. So I'm going to erase some of the drawings so I can show some work now. So let's just plug in negative five for the X. Let's just pick that one. So we'll have H of negative five is equal to negative 1/ multiplied by X squared. In this case is X. So we would have negative five squared and that will be equal to negative five squared is positive 25. So we would have negative 1/5 or negative one divided by five multiplied by positive 25 which is equal to, this would be the same as saying 25 divided by negative five, which is positive five or I'm sorry because we have a positive answer. Uh positive 25. This would have to be negative five as well because negative five time multiplied by negative five would give us to 25. So H of negative five would be negative five or the points negative five comma negative five. And now that matches with Entero B but not Entero D. Now, if we wanted to test another point, we see that they have the same origin but they differ, they differ in when what X gives a value of negative 20. So graph D reaches a point of negative 20 at X equals two. But graph B reaches that negative 20 at X equals 10. So we could also test that. So let's say we have age of 10 and we'll go with 10. Now, since B is leading up to be our answer seems like it's gonna be our answer. We'll try that point, age of 10 is equal to negative one fifth multiplied by X squared. And in this case, our X is going to be 10. So we'll plug in 10 for the X, we'll have 10 squared. So age of 10 is equal to negative 1/ multiplied by 100 since 10 squared is 100. And now this is the same as saying 100 divided by negative five. So we have age of 10 is equal to negative 20. Since negative 20 multiplied by negative five will be positive or the point 10 comma negative 20. And this once again matches up with answer choice B and does not match up with a choice D. So now we can confidently say that entry choice B will be the right graph and the answer to our question. So I hope that was helpful. And until next time.

Graph each function. See Examples 1 and 2. ƒ(x)=-(1/2)x^2

Key Concepts

Quadratic Functions

Vertex of a Parabola

Graphing Techniques

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