anonymous
  • anonymous
y=-(x+2)(x-4) find the domian,range,axis of symmetry
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@welshfella
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
first step would be to multiply this out

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anonymous
  • anonymous
Okay
misty1212
  • misty1212
let mt know what you get
misty1212
  • misty1212
then we can finish quickly
anonymous
  • anonymous
Alright, hold on:)
anonymous
  • anonymous
-x^2+2x+8
misty1212
  • misty1212
ok good
anonymous
  • anonymous
:)
misty1212
  • 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
misty1212
  • misty1212
the first coordinate of the vertex of \(y=ax^2+bx+c\) is \[-\frac{b}{2a}\] which in your case is \[-\frac{2}{2\times (-1)}\]
anonymous
  • anonymous
1
misty1212
  • misty1212
right and the second coordinate is what you get for \(y\) when you replace \(x\) by \(1\)
anonymous
  • anonymous
9
misty1212
  • misty1212
right again
misty1212
  • misty1212
so lets answer each question in order
anonymous
  • anonymous
d=all real #'s right?
misty1212
  • misty1212
Find the domian the domain of an polynomial is \(\mathbb{R}\) what you said
misty1212
  • misty1212
the range since it is a parabola that opens down, and has a maximum at \(y=9\) the range is?
anonymous
  • anonymous
y>=-9
misty1212
  • misty1212
oh no
anonymous
  • anonymous
Oh:( Ok
misty1212
  • misty1212
not sure where you got the \(-9\) from it is \(9\) right?
anonymous
  • anonymous
yes, whoops!
misty1212
  • misty1212
and also the parabola opens down that means the MAXIMUM value is 9, not the minimum value
misty1212
  • misty1212
|dw:1439235731008:dw|
anonymous
  • anonymous
is maximum <=,>= or <,>
misty1212
  • misty1212
lets forget about rules and think the possible values for \(y\) are numbers less than or equal to 9
anonymous
  • anonymous
Alright
misty1212
  • misty1212
if you want to write it as an inequality you can write \[y\leq 9\] or as an interval \[(-\infty, 9]\]
anonymous
  • anonymous
okay, I see :)
misty1212
  • misty1212
and finally, the axis of symmetry which we found ages ago is \(x=1\)
misty1212
  • misty1212
done right?
anonymous
  • anonymous
yes:)
anonymous
  • anonymous
Thank you:)
misty1212
  • misty1212
\[\color\magenta\heartsuit\]

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