Question

Select the best choice for the value f(a-2) of the dependent variable for the function f(x)=-2x^2-3x-1.

A.) y=-5a+9
B.) y=2a-3
C.) y=2a^2-11a-13
D.) y=-2a^2+5a-3

I think I kinda get the idea, but I dont understand the question. Its the beginning of the year and I plan on acing this class so I want to understand EVERYTHING.

Answer 1

okay so dependent variable is y, or f

Answer 2

so the value for the variable x is a-2.
So all they want to know is what is the value of y when x=a-2 for the equation f)x)=-2x^2-3x-1.

Answer 3

so, y=-2(a-2)^2-3(a-2)-1

Answer 4

yes
plug in x = a-2 in f(x)

Answer 5

so f=y right?

Answer 6

yes

Answer 7

simplify and see what you get

Answer 8

Alrighty. They just have to be complicated. :)
y=-2(a-2)^2-3(a-2)-1
y=-2(a^2-4)-3a-6-1
y=-2a^2-8-3a-7
y=2a^2-3a-15

Answer 9

>:/ which isn't an option.

Answer 10

you made a mistake when calculating (a-2)^2

Answer 11

hm actually in another place too, a negative number multiplied by another negative number equal a positive number

Answer 12

yes (a-2)^2 = a^2 -4x + 4

Answer 13

yes (a-2)^2 = a^2 -4x + 4 not understanding what that is...and it'd be a^2 and then 2squared is 4, so a^2-4.

Answer 14

have you learned to FOIL yet? (a-2)^2 doesnt equal (a^2) +(-2)^2, its
(a-2)(a-2)

Answer 15

FOIL? I've never heard of that.

Answer 16

= -2(a^2 -4a + 4) -3a + 5
= -2a^2 +8a - 8 - 3a+ 5
# -2a^2 + 5a - 3

Answer 17

Where did you get the 4a +4?

Answer 18

I promise I'm not trying to be stupid :)

Answer 19

ok while he explains that, I just want to clarify that

-3(a-2) = -3(a)+(-3)(-2) = -3a +6

Answer 20

(a - 2)^2 = (a - 2)(a - 2)
now multiply the second bracket by a then by -2
= a(a - 2) +2(a - 2)
= a^2 - 2a - 2a + 4
= a^2 - 4a + 4

Answer 21

second line should read
= a(a - 2) - 2(a - 2

Answer 22

alternatively you could use
http://en.wikipedia.org/wiki/FOIL_method

so (a-2)(a-2)
= a^2 -2a -2a +4
= a^2 -4a +4

Answer 23

oh okay...so let me start over then.

y=-2(a-2)^2-3(a-2)-1
y=-2[(a-2)(a-2)]-3(a-2)-1
y=-2(a^2-2a-2a+4)-3a+6-1
y=-2a^a-3a+9

Answer 24

last line should be y=-2a^2-7a+9

Answer 25

*facepalm*

Answer 26

you've gone wrong on last line
next step is to multiply the terms in the parentheses by -2

Answer 27

dont try and do too much processing at same time

Answer 28

yes yes i see that... okay AGAIN. :)

y=-2(a^2-2a-2a+4)-3a+6-1

SO, y=-2a^2+8a-8-3a+6-1

therefore... y=-2a^2+5a-3

Answer 29

Which is an option hurrah!

Answer 30

yea - you got the right option too

Answer 31

:) thank you so much, that (a-2)(a-2) helped

Answer 32

yw - you can use FOIL if you like personally i prefer the other method where you multiply the second bracket by each part of first bracket

- thats call distributing a and -2 over the (x - 2) - The distributive law

Answer 33

Okay, I'll go the long a sure route, thats the way my brain works. :)