Question

How can you write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function?

I really don't get why I have to answer these questions when none of this information is even remotely in my lessons...

Answer 1

@amistre64 @jim_thompson5910

Answer 2

what are some functions you can think of off the top of your head?

Answer 3

like one made up or?

Answer 4

well for now, just a type of function

Answer 5

what are some types?

Answer 6

um... I'm not really sure.

Answer 7

if you were to make one up, what would it be?

Answer 8

Well, I'm pretty sure a function is something like f(x) = x^2 + 8x – 16

Answer 9

that's a quadratic, and that's one type of function I had in mind

Answer 10

yeah, that's what I'm studying currently.

Answer 11

unfortunately x^2 + 8x – 16 can't be factored, but let's focus on x^2 + 5x + 6 instead

Answer 12

x^2 + 5x + 6 can be factored

Answer 13

what two numbers multiply to 6 and add to 5?

Answer 14

I don't know.

Answer 15

list out all the possible ways to multiply to 6

1*6
2*3
-3*-2
-6*-1

then add up each pair to see which one gets you 5

Answer 16

2 and 3?

Answer 17

correct

Answer 18

so that means x^2 + 5x + 6 factors to (x+2)(x+3)

Answer 19

x^2 + 5x + 6 is equivalent to (x+2)(x+3)

ie they are the same, just in different form

Answer 20

why bother with factoring? well the factored form shows us what the roots or zeros would be

x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

So you can think to yourself "after factoring, take each piece and solve for x"

Answer 21

so while x^2 + 5x + 6 tells us nothing about the roots (at least directly) the factored form (x+2)(x+3) does tell us the roots nearly directly

Answer 22

but x^2 + 5x + 6 is still useful in that we see that it's a quadratic, so we know we have a parabola as the graph. Also, the +6 at the end tells us the y-intercept

Answer 23

So, since I have to tell my teacher my answer to the original question over the phone and can't show her written work, how do I express all of that in complete sentences?

Answer 24

well I recommend reading through what I wrote a few times to help it sink in better. I also recommend you practice with factoring and solving more. After you've gotten the hang of it, then I would call the teacher up to tell him/her that. Ideally you would say it in your own words, but you can use definitions to help you out.

Example

Teacher: "Why is factoring important?"
You: "It helps us see the roots without having to do much work, if any at all"

That's a simplified example, but just imagine you're trying to explain all this to a friend.

Answer 25

Thank you, you've been a huge help. My lessons just... they don't have any shred of this information in them and it makes it hard when I have to answer questions like this.

Answer 26

Yeah the common core can be a bit odd. I agree. With more practice, it should come a bit easier.