## that1chick 2 years ago Rewrite y = 3x2 - 24x + 10 in general form.

1. Mertsj

General Form You have already seen how to graph a quadratic function when it is in its standard form. Recall that the standard form of a quadratic function looks like: y=a(x-h)^2+k But how do you graph a quadratic function when it is in its general form? The general form of a quadratic function looks like this: y=ax^2+bx+c

2. Mertsj
3. Mertsj

So how does your author define general form?

4. that1chick

h=x, k=y... the problem I'm having with this one is splitting the 3 in 3x^2...?

5. that1chick

Its just asking to rewrite it not graph it... heres what I have so far:

6. Mertsj

So you want h-k form?

7. that1chick

-10 on both sides Y-10=3x^2-24x 24/2=12 12^2=144 Y-10=3x^2-24x+144

8. that1chick

Its in standard form, I want general form(:

9. Mertsj

Let's write it like this: |dw:1362857059987:dw|

10. Mertsj

Now complete the square inside the parentheses

11. that1chick

OH! gcf! of course!!:D

12. Mertsj

|dw:1362857161791:dw|

13. that1chick

Thank you(: I forgot to look for a gcf

14. Mertsj

yw

15. that1chick

Y-10=3x^2-24x+144 Now factor the GCF y-10=3(x^2-8x+48) y-10=3(x-4)(x+12) +10 to both sides Y=3(x-4)(x+12) +10 Right?

16. that1chick

how did you get 16^^

17. that1chick

Oh wait... I know

18. Mertsj

No. You cannot add 48 to one side without adding it to the other side. Did you see in my example that I added 16 inside the parentheses to complete the square? But I was really adding 48 to the right side because there is a 3 outside the parentheses. So then I subtracted 48 so there would be a net change of 0. Of course I could have added 48 to the left side which would have accomplished the same purpose.

19. Mertsj

16 is the number that completes the square for x^2+8x

20. that1chick

1 sec..

21. that1chick

Y-10=3x^2-24x GCF Y-10=3(x^2-8x) Complete the square 8/2=4 4^2=16 y-10=3(x^2-8x-16) Simplify y-10=3(x-4)^2 +10 to both sides y=3(x-4)^2 +10 Right?

22. that1chick

and by simplify I mean find the binomial...(:

23. Mertsj

So let's multiply out your result: \[y=3(x-4)^2+10=3(x^2-8x+16)+10=3x^2-24x+48+10=\]

24. Mertsj

\[3x^2-24x+58\]

25. Mertsj

Is that the problem you started with?

26. Mertsj

If it isn't, then what you have done is changed the original problem instead of keeping the original problem and expressing it in another form.

27. that1chick

What am I doing wrong?

28. Mertsj

When you add 48 to the right side, you then have 2 choices: 1. subtract 48 from the right side 2. Add 48 to the left side.

29. that1chick

y-10=3x^2-24x y-10=3x^2-24x+48 +48 y+38=3x^2-24x+48

30. that1chick

y+38=3(x^2-8x+16) y+38=3(x-4)^2 Right so far?

31. that1chick

Ok I solved it out on paper(: thank you for helping me

32. Mertsj

yes

33. Mertsj

yw

34. that1chick

24/2=12 12^2=144........

35. Mertsj

That is true. Not sure it is very useful.

36. that1chick

y-10=3x^2-24x+144

37. that1chick

k, never mind