Question

f(x)=(-3x^2)+13x-11

Answer 1

What are you supposed to do with this? Graph it?

Answer 2

no

Answer 3

What then? You haven't posted the directions.

Answer 4

Find roots?

Answer 5

how to complete a square

Answer 6

yep

Answer 7

Hint: Since y = f(x), rewrite it like this:

\(y = -3x^2 + 3x - 11\)

Next add 11 to both sides, then divide divide both sides by -3 to get:

\(\frac{y + 11}{-3} = x^2 - x\)

Now add \(\frac{1}{16}\) to both sides to get:

\(\frac{y + 11}{-3} + \frac{1}{16} = x^2 - x + \frac{1}{16}\)

Once you have finished reducing, you should have a new expression for y

Answer 8

is that the answer

Answer 9

?

Answer 10

The final result I get comes out to

\(y = -\large\frac{48(x-\frac{1}{4}^2) - 3}{16} - 11\)

Answer 11

But that hasn't been simplified

Answer 12

How is that better than what he wrote originally?

Answer 13

Because it said to complete the square

Answer 14

Once you complete the square, you have to put it back in the form y =

Answer 15

But let me fix one minor mistake

Answer 16

\(y = -\large\frac{48(x-\frac{1}{4})^2 - 3}{16} - 11\)

Answer 17

ok

Answer 18

Ideally, I think you would want to express that as just one fraction.

Answer 19

yes

Answer 20

Well, I did most of the work for you. You can finish the rest.

Answer 21

Also, you might want to change y back to f(x)

Answer 22

ok sure

Answer 23

yes

Answer 24

\(f(x) = -\large3(x-\frac{1}{4})^2 - \frac{179}{16}\)

Answer 25

THANKS

Answer 26

hero

Answer 27

I must have made a calculation mistake because here's wolfram alpha's result:

http://www.wolframalpha.com/input/?i=complete%20square%20(%5B%2F%2Fquantity%3A-3%2F%2F%5D)x%5E2%2B(%5B%2F%2Fquantity%3A13%2F%2F%5D)x%2B(%5B%2F%2Fquantity%3A-11%2F%2F%5D)

Answer 28

Yeah, I see where I went wrong. I added 1/16 to both sides instead of adding 1/4 to both sides

Answer 29

ok