How to Write an Explicit Form From an Implicit Form

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Writing an explicit form of an implicit form will require you to look at the variables. Write an explicit form from an implicit form with help from an experienced mathematics professional in this free video clip.

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Hello, my name is Walter Unglaub, and this is how to write an explicit form from an implicit form. So if we're given an equation that is an implicit form, that means that all of the dependents on the variables is on one side of the equation, and we said it usually equaled to zero on the other side of the equation. So if we want an explicit form for this equation, let's say I want y as a function of x, then it's simply a matter of algebraically solving for y in terms of x. And this means I'm going to have to rearrange some of these terms. So, let's do that. We notice that there's just one term in this polynomial that depends on y, so I'm gonna move that over to the other side and it becomes positive, so I have positive 2y-squared is equal to 8x to the fourth power, plus 32 plus 32 time x-squared. The next step of course is to divide both sides by two, so I get rid of that factor on the left-hand side, and this simplifies to y-squared is equal to four x to the fourth plus 16 plus 16 times x-squared. Now, because I have a square here, I'm gonna want to take the square root of both sides, and because it's an even power, I'm going to have a plus and a minus as two possible solutions for my y. So I have plus minus the square root of four times x to the fourth plus four plus four x-squared. Where I have factored out a four from each of these three terms. Now this will simplify to y is equal to plus minus two, because I have the square root of four is simply equal to two, times the square root of x to the fourth plus 4x-squared plus four, and I realize that the argument inside of the square root can be written as x-squared plus two, the whole thing squared. So, the square root of this quantity right here, simply acts to remove the exponent, and I'm left with y is equal to plus minus two times x-squared plus two. So now, I have turned my implicit equation, which had terms involving x and y all on one side of the equation, and I have converted it into an explicit form, in which I have y as my dependent variable and x as my independent variable. My name is Walter Unglaub, and this is how to write an explicit form from an implicit form.

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