hhopke one year ago What is the range of function 3x^2+6x-1 in interval notation?

1. hhopke

Also, according to the HW program, $(-4,\infty)$ is wrong.

2. anonymous

the domain of all polynomial function is all real numbers.

3. hhopke

Yeah. Domain is $(-\infty,\infty)$

4. anonymous

:)

5. hhopke

But what is the range?

6. hhopke

If you plug it into a graphing calculator, it looks like this:

7. hhopke

You still there, @Photon336 ?

8. Photon336

@hhopke since it's quadratic you could use part of the quadratic formula, and see what value it is whether if it's greater than zero, this will give you a sense of it's real or imaginary. i feel that this is important because if b^2-4ac < 0 then your function is going to be imaginary, so i guess not all real numbers will apply to this. $b ^{2}-4ac$ > 0 b = 6 a = 3 c = -1 (6)^2-4(3)(-1) = 48 it's all real numbers, it's going to be continuous everywhere, every x value has a distinct y v value. my math skills are weak, but usually if a function is continuous everywhere it's also differentiable on that particular interval. if we take the derivative. $\frac{ dy }{ dx } 3x ^{2}+6x-1 = 6x+6$ that's continuous for x value.

9. hhopke

Thank you, but I have absolutely no clue what you just said. We just started this. All the information I have on the subject (and supposedly, all I need) is that if a parabola concaves up, then the range is anything greater than the Y value of the vertex, and if it concaves down, then the range is anything less than the Y value of the vertex. Really basic stuff- no quadratic formula yet. :)

10. Photon336

@hhopke yeah, sorry about that lol I thought you were asking for the range

11. hhopke

I was asking for range. Everything else I search on the internet gives me all sorts of weird stuff using set notation and such... :(

12. Photon336

so for a parabola the general formula is this: $ax ^{2}+bx+c$

13. Photon336

@hhopke the sign in front of the a value tells us whether a prabola will concave up or down

14. hhopke

Right. This one is up, b/c 3>0 right?

15. Photon336

look at this |dw:1444541020427:dw|

16. hhopke

Yeah. When I graphed it on my calculator, it gave me a concave-up parabola. The vertex was at (-1,-4). But when I tried to do the range in interval notation, I typed (-4,oo) and the program said it was wrong. ???

17. hhopke

18. Photon336

@hhopke Domain = all x values

19. Photon336

while range is all y values

20. hhopke

All possible Y-values for the function is the range of that function. The lowest possible y-value for this particular function is -4. Interval notation for the range should be (-4, oo) right? (oo is infinity)

21. Photon336

yeah I just plotted your graph on wolfram alpha. -4 is the lowest y value

22. hhopke

So what am I doing wrong? :(

23. Photon336

@ganeshie8

24. Photon336

i'm not sure, let me tag someone who knows better

25. hhopke

Alrighty. Same thing happened w/ function 3x^2. Plugged it in, lowest y-value was 0. Plugged in (0, oo) for range and it was marked wrong. :(

26. hhopke

@ganeshie8

27. hhopke

This happened with all the problems, if that helps.

28. ganeshie8

$3x^2+6x-1\\~\\=3(x^2-2x) - 1 \\~\\= 3(x^2-2x+1)-4 \\~\\= 3(x-1)^2-4\\~\\\ge -4$ therefore the range is $$[-4, \infty)$$

29. hhopke

ooooooooooooooohhhhhhhhhhhhhhh.... I formatted it wrong. Thank you sosososososososososososososo much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

30. ganeshie8

change the left parenthesis, "$$($$", to square backet "$$[$$" and you will be okay

31. ganeshie8

np, other than that ur work looks good ! nice job!

32. hhopke

THANK YOU SO MUCH TO BOTH @ganeshie8 and @Photon336

33. Photon336

in the third line, how did you get -4 @ganeshie8 ?