## anonymous 4 years ago Find the minimum value for the function: y = x^2 + 9x + 18

1. anonymous

do u knwo how to complete the square? or do u factor it?

2. anonymous

lets factor its easy

3. anonymous

its under my quadratic function lesson so idk

4. anonymous

what 2 numbers when you multiply them =18 and when u add them =9?

5. anonymous

is there a number for that?

6. anonymous

6*3=18 6+3=9

7. anonymous

ohhh

8. anonymous

so is the answer 9 ?

9. anonymous

yaaaa factoring i just taught this to my class today. hmmmm nooooo we r factoring. We r trying to figure out 2 numbers that when u mulyiply them give us 18 and when u add them gives us 9

10. anonymous

finding the zeros is a long and complicated way to find the minimum

11. anonymous

umm well we can complete the square

12. anonymous

but i dont think she knows that

13. Zarkon

use the vertex formula

14. anonymous

minimum is at the vertex, and first coordinate of the vertex of $y=ax^2+bx+c$ is always $$-\frac{b}{2a}$$

15. anonymous

when doing the vertx thing... is the second number the minimum?

16. anonymous

in your case it is $$-\frac{9}{2}$$ replace $$x$$ by $$-\frac{9}{2}$$ to find the minimum

17. anonymous

minimum means minimum value of $$y$$ so it is the second coordinate, not the first

18. anonymous

so yes, what you said, the second number is the minimum.

19. anonymous

ohhh i like this method. We never learnt this stuff. Like the textbook always made us complete the square. oh cooll

20. anonymous

can i just plug it into my graphing calculator to get the anwser ?

21. anonymous

completing the square is for suckers, unless of course you are solving a quadratic equation

22. anonymous

last i heard minimum value was in a calculus class o.O i never knew it was in algebra too

23. Lukecrayonz

It's in Algebra 2.

24. Lukecrayonz

You can use a calculator to solve it

25. anonymous

hahah its in math 11 here in canada

26. anonymous

$(-\frac{9}{2})^2+9\times (\frac{-9}{2})+18$ then a calculator if you need one

27. anonymous

you turn math up to eleven in canada? mine only goes up to ten

28. Lukecrayonz

Ti-84, input the equation into Y= then click 2nd Trace, and do minimum. It will say "Left bound?", go to the left side of the graph and press enter. Right bound? Obviously, right side. It will say "Guess?", which means put it to where you think the minimum y value is.

29. Lukecrayonz

So for this, you get x=-4.5 and y=-2.25

30. anonymous

sooo many numbers ... ahhhhh!!! >_< what about TI-83 plus?

31. anonymous

32. anonymous

so taking the derivative and equating to zero is another story?

33. Lukecrayonz

It'll be exactly the same basically I think.

34. Lukecrayonz

Yes lgb haha

35. anonymous

they give us this freshman yr. imma senior now tryna make it up.. sucks :/

36. anonymous

thanks everyone

37. anonymous

using the derivative to find the minimum value of a quadratic. like using a glock to kill a wingspanroach