![]() ![]() How wide or how narrow the opening of our We have a wider opening uÄ«ecause our scaling factor is lower than 1. Squared, we still have a parabola, but we go upĪ little bit slower. If we scale it by 2, it's stillĪ parabola with the vertex at the same place, but And let's do another one that isÄ¡.5 times our 0.- I could just do 0.4 actually. Get 2 times- no, not 2 squared -2 times x squared. Squared and see what happens when we scale it. I'm going to scale the graphsĪnd I'm going to shift them. I really didn't do this yet with the regular Result that I got over there, although mine Look, if you just focus on theįirst quadrant right here, you see that you get the exact same So first it did x squaredĪnd then it did the square root of x. The right: squared and the radical sign and all of that. The right, just so you know what I'm doing. Graph y is equal to the square root of x. Let's graph it a littleÄ«it cleaner than what I can do by hand. Especially if you're lookingÄifferent things. And hopefully, you shouldÄ«e able read this. Inverses in the future that are symmetric around the ![]() Symmetric around the line, y is equal to x. And once again, it makesĬomplete sense because we've swapped the x's and the y's. Positive quadrant, so we get this upward opening To x squared, and we've seen this before. 4 comma 16 is going toÄ«e right above there. To draw it a little bit smaller than that. Point 1 comma 1, the point 2 comma 2, which I'm going to have The positive, in the first quadrant here. I think that's instructive sometimes before you take out Have a guess of- Let me just graph them here. Swapped the x's and y's between this function and thisįunction right here, if you assume a domain of positive Only take on positive values because this is a principal To restrict the domain of y to positive y's because this can Of this equation, you would get y squared is equal When x is a 4, what is y? Well, the principal square That's negative 1, but we don't have a positive or Principal square root of x of 1 is just positive 1. Y going to be equal to? The principal square Values on purpose just to make it interesting. When y is equal to the principal square root of x. Y going to be equal to? Well y is x squared. So let me just pick someĪrbitrary x values right here, and I'll stay in the Table before we get out our graphing calculator. Understanding of what causes these functions to shift upÄown or left and right. We'll shift them around a little bit and get a better And see how it relates to theįunction y is equal to x- Let me write it over here because Is equal to the principal square root of x. ![]() What I want to talk about is the graph of the function, y The negative square roots, you'll write a plus orĪ minus sign in front of the radical sign. ![]() Or if you wanted to refer toÄ«oth the positive and the negative, both the principal and Negative square root, you'd actually put a negative in front Sign, you're actually referring to the positive square Something- A square root of 9 is a number that, if You might already know that 9 has two actual Square root, I'm really saying the positive square root of 9. Under a radical sign like this, this means the principal Sign, I think you know you'll read this as the squareĬlarification. Want to clarify some of the notation that at least, I always This is just one of infinitely many solutions.Reasonably familiar with the idea of a square root, but I Since I am typing on mobile, all the < in this post are less than or equal to. If you want the full cup, rotate about the x axis. Next the stem: Let's just have a 2cm thick shaft 6cm high, so for the stem: 0 ![]()
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