Question

f(x) = -X^2 + 6x -11 solve for f(t-3)

Answer 1

Plug in t-3 so:
\[\LARGE f(t-3)=-(t-3)^2+6(t-3)-11\]
Now just distribute, combine like terms, etc.

Answer 2

I got -t^2 +6t -38 but the solution states its -t^2 +12t -38, where did the 12t come from?

Answer 3

or is the solution on the pdf incorrect?

Answer 4

Show me your steps and how you approached the problem, then I'll let you know if you did something wrong.

Answer 5

-(t-3)^2 = -(t^2 + 9) = -t^2 - 9
6(t -3) = 6t -18
-9 + -18 + -11 = -38
f(t-3) = -t^2 +6t -38

Answer 6

Ah, there's your mistake:
\[\LARGE (a+b)^2 \ne a^2+b^2\]

Answer 7

or if it was minus:
\[\LARGE (a \pm b)^2 \ne a^2 \pm b^2\]

Answer 8

When doing \[\LARGE (t-3)^2\]
\[\LARGE (t-3)^2 \ne (t^2)+(-3)^2\]
It's actually:
\[\LARGE (t-3)^2=(t-3)(t-3)\]
So distribute this and get:
\[\LARGE t^2-6t+9\]

Answer 9

Now just distribute that negative and finish it:
\[\LARGE -(t^2-6t+9)+6(t-3)-11\]

Answer 10

-t^2 +6t -9 +6t -18 -11 = -t^2 +12t -38

Answer 11

There ya go :)

Answer 12

thank you how do you write the formula so neat when you reply?

Answer 13

At the bottom of this reply box there are four buttons right? Use the one that has the sigma and "Equation"

Answer 14

But I've been practicing it so much that I can just write it out in plain text without it.

Answer 15

Sorry for bothering with simple calculus haven't been in school for 7 years and am going back to school so am brushing up.

Answer 16

Oh, it's no problem at all, always happy to help~

Answer 17

Also:
\[\LARGE \mathbb{\color{green}{WELCOME~~TO~~OPENSTUDY~\ddot\smile}}\]

Answer 18

If you have any questions on the site feel free to shoot me a message, hope you enjoy your time here :)

Answer 19

Am going to close this question but could you break down (a+b) 2 ≠a 2 +b 2 a bit more?

Answer 20

Oh, and if you haven't already, it would be helpful to read the CoC to avoid any trouble: http://openstudy.com/code-of-conduct

Answer 21

And break it down? As in explain it?

Answer 22

(t−3)^2 =(t−3)(t−3) yes I do understand where t^2 and 9 come from but where is 6t?

Answer 23

Well when you have \[\LARGE (t-3)^2\]
It's saying t-3 squared, as in multiply it by itself. so \[\LARGE (t-3)^2=(t-3)(t-3)\]
And in that cause you would use the FOIL properties:

F-First
Outer
Inner
Last