anonymous
  • anonymous
For the function f(x) = –(x + 1)2 + 4, identify the vertex, domain, and range.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Do you mean \( \huge f(x) = (x-1)^2 + 4) \)
anonymous
  • anonymous
If you look at \( \huge f(x) = (x-1)^2 + 4) \) you can tell where the vertex is located. \( \huge f(x) = (x-1)^2 + 4) \) The 1 in \( (x-1)^2 \) is the x and the + 4 is the y so the vertex is (1,4)
anonymous
  • anonymous
It also is telling the parabola to shift to the right by 1 and go up by four so where the 1 is located is known as the horizontal shift area and the 4 is in the vertical shift area.

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anonymous
  • anonymous
What do you think is the domain and range?
anonymous
  • anonymous
Is the domain all real numbers? And the range is y greater than or equal to 4?
triciaal
  • triciaal
@Nixy a = -1
anonymous
  • anonymous
I'm unsure as to whether the vertex is truly (1,4) or if it is (-1,4). For reference, the function is f(x)=-(x+1)^2 +4
triciaal
  • triciaal
|dw:1436741859005:dw|
xapproachesinfinity
  • xapproachesinfinity
I meant all real numbers that latex did not come out good
anonymous
  • anonymous
Yes, triciaal with his equation a = -1
triciaal
  • triciaal
|dw:1436742029268:dw|
xapproachesinfinity
  • xapproachesinfinity
If f(x) is polynomial of degree n then domain is \[\mathbb{R} \]
anonymous
  • anonymous
@Thanasi99 it is (-1, 4)
anonymous
  • anonymous
Thank you so much everyone! I do believe I had it now. Vertex= (-1,4) Domain= All real numbers Y= less than or equal to 4
anonymous
  • anonymous
Correct Thanasi99
triciaal
  • triciaal
range set of y- values domain set of x values vertex maximum or minimum here you have a max at 4 when a is positive opens up when a is negative opens down
xapproachesinfinity
  • xapproachesinfinity
The range you get from the min / max if parabola mainly looking at the y value of the vertex and considering the value of a positive or negative
xapproachesinfinity
  • xapproachesinfinity
I meant the values of a parabola open up or down will tell pretty much about range
anonymous
  • anonymous
So, considering the parabola maxes out at 4 on the y-axis, and continues infinitely downward, the value set for the range would be y (less than or equal to) 4?
xapproachesinfinity
  • xapproachesinfinity
Max 4 means that is great most x can map to. So all values if y that are less than or equal to that are good
xapproachesinfinity
  • xapproachesinfinity
Sorry for some English typos from my phone lol

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