Question

Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = −x2 + 2.5x + 1. What do the solutions of 0 = −x2 + 2.5x + 1 represent on the graph of the equation?

Answer 1

So, have you learned that where the graphs of parabolas intersect the x-axis, those are the "zeroes" of the function?

Answer 2

@OakTree Yeah but i have this trouble to where when i learn something new I forget others method so sometimes its hard to memorize how u slove the answer :/

Answer 3

Okay. I totally understand where you're coming from.

What you need to know to solve this is a very simple concept that you could figure out yourself if you thought hard enough. Should I take you through the understanding part or just straight out give you the answer? I know some people like to go slow, but you might be in a hurry...

Answer 4

understanding would be great cuz i actually want to learn

Answer 5

@OakTree

Answer 6

OK - sorry, I'm switching between two people right now.

What exactly does it mean for something to be a zero of a function? Try to explain it in your own words.

Answer 7

Its where it intersect or get the x by its self?

Answer 8

Yeah, but it also means where the function has a value of...? Like, if you plug in a value for x that isn't a zero, we get some number, but if we plug in a zero, the math machine plops out the number...?

Answer 9

And by plugging in a zero, I mean a zero of the function, not the number 0.

Answer 10

+ or -? and wouldn't it still be the same or equal +?

Answer 11

@OakTree

Answer 12

It would be 0. Think about it and tell me when you get it.

Answer 13

the answer would be 1 if we were to put the number 0 right?

Answer 14

I mean, if we put a zero of the function, or a solution to the function, in as our value of x, we would get an answer of zero. Let me give you an example.

Say our function is f(x) = x^2 -1. Our zeroes are 1 and -1. If we plug 1 and -1 into the function as x, we get 0 both times. See?

Answer 15

Oh wow makes alot of sense @OakTree

Answer 16

and I apologize I had a issue with my body medicine side effects

Answer 17

That's fine. I hope you feel better now! Anyway, so we're on the same page. That's good.

Now let's take it to the next step. We know that the solutions (I'm just going to use solutions from now on instead of zeroes - it'll prevent confusion) of a function give us a value of zero. But it's in the form f(x)=0, or y=0. So say, like in the previous example, we plug in x=1 and we get y=0. This is, in essence, the ordered pair (1,0)!

But what can we say now? We know that no matter the function, when we plug in a solution, we will get an ordered pair like (x,0). So all the solutions will always be along the x-axis, because that's where the y-value is always 0. Make sense?

Answer 18

Yeah u explained alot better than my last year teacher lol

Answer 19

:) Anyway, so that's why the solutions of a function will always be at the intersections of the x-axis. So back to the original question. Using graphing technology, we can pinpoint the exact point where the graph goes through the x-axis, and at those points, the x-values are the solutions. And that's the LONG answer to your question.

Answer 20

Thank you so much I hope one day if i get stuck I could ask for ur assistant someday ^^

Answer 21

No problem. Just put me down as a fan and write a testimonial or something, and that way you can grab me next time.

Answer 22

Thanks. And so you know, you can always use wolframalpha.com to solve these kinds of problems for you if you ever get stuck. Just don't get too dependent. :)