Question

What is the average rate of change for the relation shown below between x = -2 and x = 2

Answer 1

@Tommynaut

Answer 2

Your questions are just getting more weird

Answer 3

I think you might be able to work it out by turning it into an equation, then finding the derivative (have you learnt calculus yet)?

Another way would be to understand what the rate of change means, and to see how it changes along the curve between those points

Answer 4

how so? lol
and no this is just algebra 2

Answer 5

Hmm I'm guessing that's in the US system? I'm only familiar with the levels in NSW Australia to be honest. In any case, do you know what the rate of change is, graphically?

Answer 6

would it be like a slope? rise over run. It says to write it as a fraction/ratio

Answer 7

Yeah, that's pretty much it. It's the slope at any point on the function; to imagine it, just think of a line tangent to a point and see how much it slopes (which you always look at from left to right).
In your scenario, if you look at the slope at x = -1, you might see that it's more steep than at x = 0, but both are going down from left to right, which means both have a negative slope (also known as gradient).

Answer 8

I'm still confused because of the parabola part

Answer 9

I'm just confused because of the question itself - I don't recall ever doing a question quite like this but maybe some that were similar.

I'm also not sure what sort of methods you would have learnt to deal with these situations/questions but, if it helps, I could tell you my perspective:
At x = -2, we can see that we have a steep negative gradient, which means it's a relatively big (but not THAT big) negative number (say, -8 for example). At x = -1, we still have a negative gradient but it's slightly less steep than at x = -2, so it would be a slightly smaller negative number (-4, for example).
By the time we get to x = 1, which is the parabola's vertex, the gradient (or slope) will be 0 because we have a horizontal line. Then, between x = 0 and x = 2, we start getting a positive slope.

Does that all make sense?

Answer 10

I agree it is a very strange question? can we do another I can always ask him about it.

Answer 11

To find the average rate of change, or average gradient, or average slope, between x = -2 and x = 2, we would have to find to find the gradient at each point, add them all up and divide by how many points we used (because that's the standard way of finding an average).
The problem is, there's an infinite amount of points between them (like, we could have x = 1.0000001 and stuff like that).

So, what we probably have to do here is much, much more simple. Maybe it's just the rise/run (= gradient) of the entire left side of the parabola, added to the rise/run of the right side, and dividing that by 2.

Answer 12

So, maybe -9/3 + 1/1, all divided by 2.

Answer 13

Sure, go for it, but it might have to go afterwards

Answer 14

mkayyy and darn your like super super helpful.

Answer 15

Thanks, I'm a maths tutor part-time so it's something I like to do, I guess :P