Graph each function. See Examples 1 and 2. h(x)=√(4x)

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Hello everybody. I hope we're doing all right. Today, today we're gonna be looking at this que math question that's telling us for the following function sketch its graph where the function is G of X equal to the square roots of 25 X. Now the answer choices that they provide us are a, a graph of a half of a Parabola almost opening up to the left hand side on the second quadrant with the points negative 25 comma 25 negative comma 50 answer choice B once again being kind of a half Parabola opening up to the left hand side on the third quadrant with the points negative 25 comma negative 25 negative 100 comma negative 50 answer choice C is again a half Parabola opening up towards the right hand side of a Cartesian plane opening up on quadrant four with the points 25 comma negative 25 100 comma negative 50. And finally answer choice D opening up in the four first quadrant on the right hand side with the points 25 comma 25 100 comma 15. Now the first thing we wanna do when looking at an equation like this, we see that we have the square root of 25 X and 25 has a square root itself. So we can simplify this a little bit. Well, the square root of 25 is five. So we can bring that out of the equation. So we would have G of X is equal to five. Since we brought it out of the square root multiplied by the square of X, we can't simplify the squared of X. So that has to stay inside the square root, but we're able to bring out the five. So now we can just think about this as what's the parent function here, right? We only, we have a five in front of the square root of X. So this is just if we know what the graph of the squared of X is, then we know where this is gonna look like. Um even even though we have a five in front of it, the five is just gonna affect the values of the graph. But at the end of the day, this is gonna be a, a graph of the squared of X with different values because it's being multiplied by five. Now, to test those values, we can just do some plugging in. So we know we're gonna have a square root of a number. So we want to plug in numbers into that X that have a perfect square. So let's do exactly that. We'll make a X and a Y table and let's just plug in perfect square. So we'll have a zero. We know zero is gonna be zero, right? If you plug in zero for X, the squared of 00 and five multiplied by zero is zero. Now, what are other perfect squares? We have four, nine, 16 and 25 let's stop it right there for now. Now, if we plug in four for our X, we'll have five multiplied by the square of four, which is five multiplied by two because the square of four is two, which equals 10. So if you plug in four for our X, we would get a result of 10 for A Y. Now for nine, if you plug in nine, you would have five multiplied by the squared of nine, which is equal to five multiplied by three because squared of minus three and that would be equal to 15. So if you plug in a nine for our X, we get a 15 for our Y. And finally, if you plug in 16, you would have five multiplied by the square root of 16, which is equal to five, multiplied by four, equal to 20. So if you plug in a 16, 4 X, you get a Y of 20. And now if you plug in a 25 for the X, you have five multiplied by the squared of 25. Which is equal to five, multiplied by five and that is equal to 25. So if you plug in an X of 25 you also get a Y of 25. So now we have some points to start plugging in and I'll write them out here. We'll have zero comma zero four, comma 10 nine, comma 15 16, comma and 25 comma 25. So let's compare this with the answer choices. They gave us a choice. A is a half paralos or a graph in the relatively same shape as the squared of X. However, it's opening up to the left hand side. So if you plugged in, let's say negative XS, in this case, you would not be able to do that because you, if you plug in a negative X value for a function, you can't take the square root of a negative number unless you're working with imaginary numbers, which were not in this case. And a point that they also provide us is negative 25 comma 25 which is not one of the points that we obtained. So we can eliminate answer choice A right away. Now we can move on to enter choice B once again, this is opening up towards the left hand side. So again, plugging in negative XS will not be possible because once again, we can't take the square root of a negative number unless we're working with imaginary numbers, which we are not. And one of the points that they provide us is negative 25 comma negative which is also not a point we obtained. So we can eliminate that answer choice as well. So now we can move down a bit and look at A C as choice C is opening up towards the right hand side. So you would be plugging in positive Xes. However, if you're plugging in a positive X, you would not obtain a negative answer as your result in this case. And one of the points that they provided us is 25 comma and negative 25. But we have positive 25 comments, positive 25. So once again, we could eliminate this because it does not match our points. And finally, we have answer choice D opening up in the first quadrant. So a positive axis which we are able to plug into our equation. And one of the points that they have is 25 comma 25 which, which is a point that we obtained. So that checks out. So the other point that they have is 100 comma 50. So that's something else that we could try. Once again, we had our function as G of X is equal to five multiplied by the squared of X. So they have the X of 100. So let's try that ourselves. Now we would have of is equal to five multiplied by the square root of 100 which is equal to five multiplied by 10, which is equal to 50 which would give us the 0. comma 50. And that also matches with the other point that they provided us. And I'm sure the, so we can confidently say that answer choice D is the graph and the correct answer for this question. So I hope that was helpful. And until next time.

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Graph each function. See Examples 1 and 2. h(x)=√(4x)

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