Question

Having some trouble factoring. I think I'm using the wrong factoring method, or that it can't be factored. The function I need to factor is f(t) = -16t^2 - 32t + 384.

Answer 1

f(t) = -16t^2 - 32t + 384
= -16(t^2 +2t -24)
can you now

Answer 2

Would this be the correct first step to that?

-16(t^2 + 2t - 24).

Answer 3

Oh. So that is the correct first step?

Answer 4

yup

Answer 5

= -16(t^2 +2t -24)
= = -16(t^2 +6t -4t -24)

Answer 6

It's supposed to be like that, next? It IS asking me to "Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function," but is that really how it is then? If so, what does it mean, exactly?

Answer 7

@matricked Where in the world did you get that -4t?

Answer 8

-24 = 6 x-4

Answer 9

@matricked, so where is the t?

Answer 10

If you're trying to get negative twenty-four, why still leave it in the expression?

Answer 11

= -16(t^2 +2t -24)
=-16 (t^2 +(6-4)t -24)

Answer 12

Oh, I see. Your parens are messed up. You mean \[-16(t-4)(t+6)\] For the factored product.

Answer 13

...That would make a lot more sense.

Answer 14

@FrostFelon Yeah, I've never seen anyone factor that way. I makes sense if you were used to it. He is basically solving the problem, but instead of factoring, inserts the two terms where they are multiplied.

Answer 15

Then factors simplifies I assume.

Answer 16

=-16 (t^2 +(6-4)t -24)
= -16 ( t^2 +6t -4t -24)
=-16( t(t+6) -4(t+6))
=-16(t+6)(t-4)

Answer 17

That actually takes longer than the leap of logic I usually use.

Answer 18

That is super messed up. If it works for you, fine I guess, but you have not written what you think you have.

According to your last step you have \[f(x)=-16(t^{2}+6t)+(-4t-24)\]

Answer 19

Last step before you give -16(t+6)(t-4).

Answer 20

Opps sorry; \[f(x)=-16((t^{2}+6t)+(-4t-24)\]
So,
\[f(x)=-16t^{2}+-96t+48t+384\]
\[f(x)=-16t^{2}-48t+384\]

Answer 21

There's another part of the problem that I'm not entirely sure about.

Answer 22

Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph?

I can easily tell if it's a maximum or a minimum, but I don't know how to complete the square.

Answer 23

The vertex is (-1, 400), right?

Answer 24

@FrostFelon, Little late, but I believe complete the square means find t and solve \[16t^{2}\]

Answer 25

Oh.