Question

Using variable substitution, how do I find the expression for y^2 - 2y + 3, if y = 4 + h

Answer 1

replace y with (4+h) and expand

Answer 2

you should get a quadratic in terms of h, then test the solutions to see if you have to abandon one of them

Answer 3

(4+h)^2 - 2(4 + h) + 3

Answer 4

thats the first step yes

Answer 5

I got 16 + h^2 - 5 - 2h

Answer 6

we could prolly use that as is :)

\[4+h = \frac{2\pm\sqrt{4-4(3)}}{2}\]

Answer 7

So that is the final answer? Is my answer right though?

Answer 8

(4+h)^2 - 2(4 + h) + 3

16 +8h +h^2 -8 -2h + 3

11 +6h +h^2

Answer 9

\[h=\frac{-6\pm\sqrt{36-4(11)}}{2}\]

Answer 10

Thanks!

Answer 11

but the expression is the expansion itself

Answer 12

So if I wanted to do a question like 3m^2 - 7, if m = 1 - k, what would I do?

Answer 13

same thing, replace ms by (1-k) and expand it out

Answer 14

so it would be 3(1 - k) (1 - k) - 7

Answer 15

yes

Answer 16

So what would the result be if I expand that? Sorry, I am bad with this stuff!

Answer 17

give it a try, since practice makes perfect

Answer 18

I keep on forgetting what to do with the 3

Answer 19

either use it first in the multiplication process, or use it last ...

Answer 20

abc = (ab)c = a(bc) = (ac)b

Answer 21

I don't really get it

Answer 22

It's okay. Got it

Answer 23

The answer is 3k^2 - 6k - 4

Answer 24

3*(4*6) = (3*4)*6

yes, that looks correct

Answer 25

:) Thanks!

Answer 26

good luck