Name: 圖解方程：介紹｜代數2｜Khan Academy (Solving equations by graphing: intro | Algebra 2 | Khan Academy)
Uploaded: 2021-01-14T10:33:49.000Z
Duration: 4 min 27 s
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- [Instructor] We're told, this is the graph

Use the graph to find an approximate solution

So pause this video and try to do this on your own

So they already give us a hint of how to solve it.

They have the graph of y is equal to 3/2 to the x.

And this gives us a hint, and especially because it's,

they want us to find an approximate solution,

or approximate a solution to this equation through graphing.

And the way we could do that is we could take

each side of this equation and set them up as a function.

We could set y equals to each side of it.

So if we set y equals to the left-hand side,

And if we set y equal to the right-hand side,

And what's interesting here is if we can find

the x-value that gives us the same y-value

well that means that those graphs are going to intersect.

And if I'm getting the same y-value for that x-value

And so we could look at where they intersect

and get an approximate sense of what x-value that is.

it looks like x is roughly equal to four.

And if we wanted to, and we'd be done at that point.

If you wanted to, you could try to test it out.

You could say, "Hey does that actually work out?

"3/2 to the fourth power, is that equal to five?"

It gets us, it gets us pretty close to five.

So it's not exact, but it gets us pretty close.

that could really zoom in and zoom in and zoom in,

you would get a value, you would see that x is

The key here is that we can approximate solutions

of y is equal to, so we have this third-degree polynomial

Use the graph to answer the following questions.

x to the third minus two x squared minus x plus one

Pause this video and try to think about that.

Well when we think about solutions to this,

we could say, all right, well let's imagine two functions,

one is y is equal to x to the third minus two x squared

minus x plus one, which we already have graphed here.

or the other function is y is equal to negative one.

And then how many times do these intersect?

That would tell us how many solutions we have.

that means we have a solution to our original equation.

And they intersect one, two, and three times.

How many solutions does the equation all of this business

Well same drill, we could set y equals to

x to the third minus two x squared minus x plus one.

And then we could think about another function,

Well y equals two would be up over there,

And we could see it only intersects y equals

So this is only going to have one solution.

So the key here, and I'll just write it out,

and these are screenshots from the exercise

on Khan Academy where you'd have to type in one,

or in the previous example, you would type in four.

But these are examples where you can take an equation

and then think about where they intersect.

Because the x-values where they intersect

will be solutions to your original equation.

And a graph is a useful way of approximating

what a solution will be, especially if you have

a graphing calculator or Desmos or something like that.

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圖解方程：介紹｜代數2｜Khan Academy (Solving equations by graphing: intro | Algebra 2 | Khan Academy)

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