How To: Graph square root functions & inequalities

On Yay Math, Robert Ahdoot, founder of Yay Math, will show you some square root functions and some inequalities. He begins with the problem y=x². Then he makes a sketch with two intersecting lines in a t shape. The problem is illustrated by a curved U shape, the U's bottom resting on the horizontal bar, which represents x, while the center takes the vertical line. The vertical bar represents y. This U is directed up because the x² is a positive number. If the number were negative, the U would be in the other direction under the horizontal line. In this problem you can take the square from the x and add it to the y like this: y²=x. The second example will have the horizontal line in the center of the U shape and the vertical line at its base, being a positive number it goes to the right, or opens to the right. So positive numbers either open upward or the right. A vertical line should not be able to touch the curved line in two places. In the first diagram, a vertical line (hold a pencil to it) does not touch in more than one place, while in the second example of y²=x, it does. The first example is a function and the second is not. The second equation needs to be made a function, and how to do this is by getting the square root on both sides. This will create y equals the square root of x and on the illustration the U shape will only show on the top half because the y is positive and the square root is minus or negative, which is imagined on the t-diagram. The whole lesson is graphing problems correctly. A square root has a T shape through the curve while other problems are linear in shape when graphed. By setting the variables of a problem to zero, you will get the intercept of the alternate component. With x at 0 you find the y intercept, and with y at 0 you find the x intercept. He solves the equation y = the square root of 3x + 4 here.

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