Question

can someone help me with this graphing question? image attached

Answer 1

there are 3 questions to this graph
1, how many solutions are there
2, how many positive solutions are there
3, One solution to the system of equations shown below occurs at approximately (_____, 2.75).

Answer 2

Some background:

Firstly, a "solution" just means a place where the two graphs intersect.

Normally when we talk about solutions we talk about the "roots" of an equation (which is pretty much the same thing), like y = x^2 - 4. In that situation, it's where the lines y = 0 and y = x^2 - 4, and we know y = 0 is the x axis, so we're just looking for the x values where y = x^2 - 4 crosses the x axis.

So when we have two different functions, we could call when y = f(x) and y = g(x)... we're just saying they're both some functions of x. Then, to find the x values where they meet, we put f(x) = g(x).

When we're given their graphs, we can just LOOK at the graphs to find our answers.

First off though, the parabola that's on its side isn't technically a function, because it has 2 y values for almost every x value (except at its vertex).

Answer 3

so there would be 6 solutions

Answer 4

To more directly answer your question:

1) Count how many times they intersect
2) This question is a little ambiguous because usually solutions are just considered to be the x values that satisfy both equations (or, the x values at the intersections). However, all of the intersections are on the negative side of the x axis... meaning there aren't any solutions with positive x values
3) A point is normally in the form (x,y), so what is the x value when the y value is 2.75?

Answer 5

Yes, it seems like there'd by 6 solutions

Answer 6

Great! and there would be one that is negative so there would be 5 positive ones?

Answer 7

Well, I'm not sure about that one to be honest. Is the question asking for solutions that are positive with respect to y, or with respect to x?
Normally, the solutions are with respect to x (for example, the solutions of y = x^2 - 4 are x = 2 and x = -2). So in this situation, there would be 0 positive solutions.

However, if they WERE talking about positive solutions with respect to y, then yes, there would be 5.

Answer 8

it doesn't say

Answer 9

Then I would assume it means with respect to x

Answer 10

that's so strange, ill have to message my teacher about that

Answer 11

Ok. Do you understand the rest of the question?

Answer 12

I believe so, I would just plug in the x?

Answer 13

is there any way you could help me with another c: sorry if im bothering you lol

Answer 14

Well, for the third part, you're looking for an x value, given it's y value. So you just navigate yourself to y = 2.75, and try and see what the value is at that height, for where the solutions are intersecting

Answer 15

Yeah go for it :)

Answer 16

Thank you so much!!!!!

Answer 17

Happy to help