If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Transforming the square-root function. Graphs of square-root functions. Practice: Graphs of square and cube root functions.

Current timeTotal duration Google Classroom Facebook Twitter. Video transcript I think you're probably reasonably familiar with the idea of a square root, but I want to clarify some of the notation that at least, I always found a little bit ambiguous at first. I want to make it very clear in your head.

If I write a 9 under a radical sign, I think you know you'll read this as the square root of 9. But I want to make one clarification. When you just see a number under a radical sign like this, this means the principal square root of 9. And when I say the principal square root, I'm really saying the positive square root of 9. So this statement right here is equal to 3. And I'm being clear here because you might already know that 9 has two actual square roots.

By definition, a square root is something-- A square root of 9 is a number that, if you square it, equals 9. Negative 3 is also a square root.

But if you just write a radical sign, you're actually referring to the positive square root, or the principal square root. If you want to refer to the negative square root, you'd actually put a negative in front of the radical sign.

That is equal to negative 3. Or if you wanted to refer to both the positive and the negative, both the principal and the negative square roots, you'll write a plus or a minus sign in front of the radical sign.Enter a problem Precalculus Examples Popular Problems.

Find the domain for so that a list of values can be picked to find a list of pointswhich will help graphing the radical. Set the radicand in greater than or equal to to find where the expression is defined. The domain is all values of that make the expression defined.

Interval Notation:. To find the radical expression end pointsubstitute the valuewhich is the least value in the domaininto. Replace the variable with in the expression. Simplify the result. Remove parentheses.

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Pull terms out from under the radical, assuming positive real numbers. The final answer is. The radical expression end point is.

### How to Grade Using a Square Root Curve

Select a few values from the domain. It would be more useful to select the values so that they are next to the value of the radical expression end point.

Curving a Grade - A simple and Fair Formula

Substitute the value into. In this case, the point is. Any root of is. The square root can be graphed using the points around the vertex.

At Desmos, we imagine a world of universal math literacy and envision a world where math is accessible and enjoyable for all students. We believe the key is learning by doing. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series.

Sliders make it a breeze to demonstrate function transformations. It's intuitive, beautiful math. And best of all: it's completely free.

Features: Graphing: Plot polar, cartesian, or parametric graphs. Sliders: Adjust values interactively to build intuition, or animate any parameter to visualize its effect on the graph. Tables: Input and plot data, or create an input-output table for any function.

Statistics: Find best-fit lines, parabolas, and more. Graph Maclaurin Series okay, all kinds of Taylor Series, but that guy gets no love Evaluate a definite integral int in an instant, or plot an integral with varying bounds.

Zooming: Scale the axes independently or at the same time with the pinch of two fingers, or edit the window size manually to get the perfect window. Points of Interest: Touch a curve to show maximums, minimums, and points of intersection.

Tap the gray points of interest to see their coordinates. Hold and drag along a curve to see the coordinates change under your finger. Scientific Calculator: Just type in any equation you want to solve and Desmos will show you the answer. It can handle square roots, logs, absolute value, and more.The square root grading curve is a method for raising the grades of an entire class to bring them into closer alignment with expectations.

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It can be used to correct for unexpectedly difficult tests or as a general rule for difficult classes. It adds more points to lower scores, but will not result in any scores above or in lower raw scores being curved to exceed higher raw scores. Take the square root of the raw score. Round the result to one decimal place beyond the scores recorded in your grade book. For example, if you typically grade to one decimal place, a raw score of 88 would result in the square root 9.

Multiply the square root of the raw score by 10 to get the curved score.

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In the example above, the final score would be The square root curve can be applied more than once if necessary. Low scores will continue to be more greatly affected than high scores, and high scores will not exceed percent. The square root curve may not work as intended if you are not using a point grading system. Grades should always be expressed as a percentage value when using this curve. Copyright Leaf Group Ltd.I just made my first Marbleslides in Desmos!

It was incredibly easy, and the students said it was a really fun way to learn. For this activity I used the absolute value, quadratic, square root, and cube root functions. I felt this activity accomplished both, and my students really seemed to enjoy it.

I have provided the activity and the worksheet for you to try. I would love feedback! Desmos Introduction to Transformations Marbleslides. I absolutely love this! Thanks for sharing it â€” I am looking forward to using it with my Algebra 2s later this year. Nice job! Also, and I really like the MarbleSlides, I find students just doing trial and error each time and not thinking about it.

What if you included a pic screenshot of a MarbleSlide every few slides and have the students predict the change in the equation without being able to test it out?

They could also explain their thinking. You could do multiple choice and give them a few options. When they chose a multiple choice, they have to explain why they picked that one. The teacher dashboard shows the results nicely too.

Oh, and I get uncomfortable when someone calls the numbers from fractionsâ€¦ sorry. I really did like your Activity Builder. I would totally use it in my class. Hi Julie and Kaleb, I am currently working through the secondary education program at the University of Illinois at Urbana-Champaign and we have also done a lot of work creating various lessons around the use of Desmos as well.

One thing that I have found to be one of the best things about Desmos is how well it is designed for students to make explorations and conjectures regarding transformations of functions in the coordinate plan. When I was supposed to create a Desmos activity for a hypothetical lesson that I would have given, I decided to frame it by telling students that they were chosen to design new rollercoasters based off of the form of linear, quadratic, absolute value, square root, cube root, and sine functions.

One of the difficult things that I found when I was making this activity was how I could possibly make a connection to some kind of real-world application. So any advice would be appreciated! Thanks for sharing. You are commenting using your WordPress. You are commenting using your Google account.You can pretty easily use parametric equations to rotate a function through any angle of rotation.

Check out this example!

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Click on the image of the graph and it will take you to the full, rotating version on Desmos! Check out this graph I made purely for the fun of it using the idea of rotations!

To find out more, including how to control cookies, see here: Cookie Policy.You only need to enter one of each grades if there are multiples of the same score. Duplicates are stripped out. But it did tell me that even though the student earns their points, a teacher has the option of working the numbers as they see fit.

I prefer to use a linear grade distribution instead, scaling the top grade to a and the low grade to a 50; assuming that there are grades under a His post goes over several curve types, including my personal favorite the gravity curve, and also discusses why you would curve an exam.