## tbrooks3 3 years ago Find the minimum value for the function: y = x^2 + 9x + 18

1. samjordon

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

2. samjordon

lets factor its easy

3. tbrooks3

its under my quadratic function lesson so idk

4. samjordon

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

5. tbrooks3

is there a number for that?

6. samjordon

6*3=18 6+3=9

7. tbrooks3

ohhh

8. tbrooks3

so is the answer 9 ?

9. samjordon

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. satellite73

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

11. samjordon

umm well we can complete the square

12. samjordon

but i dont think she knows that

13. Zarkon

use the vertex formula

14. satellite73

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

15. tbrooks3

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

16. satellite73

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

17. satellite73

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

18. satellite73

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

19. samjordon

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

20. tbrooks3

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

21. satellite73

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

22. lgbasallote

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. samjordon

hahah its in math 11 here in canada

26. satellite73

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

27. satellite73

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. tbrooks3

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

31. samjordon

32. lgbasallote

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. tbrooks3

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

36. tbrooks3

thanks everyone

37. satellite73

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