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

1. Hero Group Title

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

2. shivraj Group Title

no

3. Hero Group Title

What then? You haven't posted the directions.

4. zepp Group Title

Find roots?

5. shivraj Group Title

how to complete a square

6. shivraj Group Title

yep

7. Hero Group Title

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 Group Title

9. shivraj Group Title

?

10. Hero Group Title

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

11. Hero Group Title

But that hasn't been simplified

12. Romero Group Title

How is that better than what he wrote originally?

13. Hero Group Title

Because it said to complete the square

14. Hero Group Title

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

15. Hero Group Title

But let me fix one minor mistake

16. Hero Group Title

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

17. shivraj Group Title

ok

18. Hero Group Title

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

19. shivraj Group Title

yes

20. Hero Group Title

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

21. Hero Group Title

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

22. shivraj Group Title

ok sure

23. goformit100 Group Title

yes

24. Hero Group Title

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

25. shivraj Group Title

THANKS

26. shivraj Group Title

hero

27. Hero Group Title

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 Group Title

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

29. shivraj Group Title

ok