Name: Solving equations by graphing | Algebra 2 | Khan academy
Uploaded: 2020-03-27T17:40:49.000Z
Duration: 4 min 19 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Instructor] Let's say you wanted to solve this equation,

Pause the video and see if you can solve this.

Well you probably realize that this is not so easy to solve.

The way that I would at least attempt to tackle it is,

you would say this is two to the x squared minus three

I could rewrite this, this is one over x to the 1/3,

Maybe I can simplify it by raising both sides

So it would be two to the negative three x squared

I just multiplied both of these terms times negative three,

is equal to x to the negative 1/3 to the negative three.

Negative 1/3 times negative three is just 1,

So it looks a little bit simpler, but still not so easy.

I could try to take log base two of both sides

and I'd get negative three x squared plus nine

But once again not havin' an easy time solve this.

And the reason why I gave you this equation

But we have other tools, we have things like computers,

is we can say hey, well what if I had one function

or one equation, that was y is equal to two x,

two to the x squared minus three I should say.

and then you could see where they intersect.

that means two to the x squared minus three

is giving you the same y as one over the cube root of x.

Or another way to think about it is they're going

where these two expressions are equal to each other.

to a graphing calculator, or we could go to a site

like Desmos and graph it and at least try

to approximate what the point of intersection is,

So I graphed this ahead of time on Desmos.

So you can see here, this is our two sides of our equation

but now we've expressed each of them as a function.

Right here in blue we have two, we have f of x,

or I could even say this is y is equal to f of x which

is equal to two to the x squared minus three.

And then in this yellowish color I have y

And we're not going to get an exact answer,

and on a tool like Desmos you can keep zooming in

in order to get to get a more and more precise answer.

and it'll even tell you where they intersect.

We can see that the x value, right over here

let's see this is 1.5, and each of these is a tenth.

it's about two thirds of the way to the next one.

And if you were to actually find the exact solution,

you would actually find this awfully close to 1.66.

or restate your problem or reframe your problem

You can set this up as, hey let's make two functions,

and then let's graph them and see where they intersect

And the x value where they intersect well

that would be a solution to that equation,

and that's exactly what we did right there.