## shivraj 3 years ago f(x)=(-3x^2)+13x-11

1. Hero

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

2. shivraj

no

3. Hero

What then? You haven't posted the directions.

4. zepp

Find roots?

5. shivraj

how to complete a square

6. shivraj

yep

7. Hero

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

8. shivraj

9. shivraj

?

10. Hero

The final result I get comes out to $$y = -\large\frac{48(x-\frac{1}{4}^2) - 3}{16} - 11$$

11. Hero

But that hasn't been simplified

12. Romero

How is that better than what he wrote originally?

13. Hero

Because it said to complete the square

14. Hero

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

15. Hero

But let me fix one minor mistake

16. Hero

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

17. shivraj

ok

18. Hero

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

19. shivraj

yes

20. Hero

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

21. Hero

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

22. shivraj

ok sure

23. goformit100

yes

24. Hero

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

25. shivraj

THANKS

26. shivraj

hero

27. Hero

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)

28. Hero

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

29. shivraj

ok