## anonymous one year ago y=-(x+2)(x-4) find the domian,range,axis of symmetry

1. anonymous

@welshfella

2. misty1212

HI!!

3. misty1212

first step would be to multiply this out

4. anonymous

Okay

5. misty1212

let mt know what you get

6. misty1212

then we can finish quickly

7. anonymous

Alright, hold on:)

8. anonymous

-x^2+2x+8

9. misty1212

ok good

10. anonymous

:)

11. misty1212

now the fact that the leading coefficient it negative ( it is $$-1$$) means this parabola opens down all that is left is to find the vertex

12. misty1212

the first coordinate of the vertex of $$y=ax^2+bx+c$$ is $-\frac{b}{2a}$ which in your case is $-\frac{2}{2\times (-1)}$

13. anonymous

1

14. misty1212

right and the second coordinate is what you get for $$y$$ when you replace $$x$$ by $$1$$

15. anonymous

9

16. misty1212

right again

17. misty1212

so lets answer each question in order

18. anonymous

d=all real #'s right?

19. misty1212

Find the domian the domain of an polynomial is $$\mathbb{R}$$ what you said

20. misty1212

the range since it is a parabola that opens down, and has a maximum at $$y=9$$ the range is?

21. anonymous

y>=-9

22. misty1212

oh no

23. anonymous

Oh:( Ok

24. misty1212

not sure where you got the $$-9$$ from it is $$9$$ right?

25. anonymous

yes, whoops!

26. misty1212

and also the parabola opens down that means the MAXIMUM value is 9, not the minimum value

27. misty1212

|dw:1439235731008:dw|

28. anonymous

is maximum <=,>= or <,>

29. misty1212

lets forget about rules and think the possible values for $$y$$ are numbers less than or equal to 9

30. anonymous

Alright

31. misty1212

if you want to write it as an inequality you can write $y\leq 9$ or as an interval $(-\infty, 9]$

32. anonymous

okay, I see :)

33. misty1212

and finally, the axis of symmetry which we found ages ago is $$x=1$$

34. misty1212

done right?

35. anonymous

yes:)

36. anonymous

Thank you:)

37. misty1212

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