anonymous
  • anonymous
Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph of y = −3x2 − 3x + 4. Show all work for full credit. Part 2 − Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −3x2 − 3x + 4.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you know how to find the vertex?
anonymous
  • anonymous
First of all the coefficient of \[x ^{2}\] is negatif (i.e -3)
anonymous
  • anonymous
so the parabola has an maximum

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More answers

anonymous
  • anonymous
you have to find the roots using the quadratic formula
anonymous
  • anonymous
\[x _{1,2}=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a}\]
anonymous
  • anonymous
x1=\[\frac{ 3+\sqrt{9-4(-3)4} }{ 2(-3) }\]
anonymous
  • anonymous
x1=-1.75
anonymous
  • anonymous
x2=0.75
anonymous
  • anonymous
|dw:1371566396504:dw|
anonymous
  • anonymous
|dw:1371566520492:dw|
anonymous
  • anonymous
line of symmetry pass through the midlle way between the roots
anonymous
  • anonymous
\[x _{line of symmetry}=\frac{ -1.75+0.75 }{ 2 }=-0.5\]
anonymous
  • anonymous
now place this value of x in your eq: \[y _{vertex}=-3*(-0.5)^{2}-3*(-0.5)+4=4.75\]
anonymous
  • anonymous
Vertex=(-0.5; 4.75)
anonymous
  • anonymous
|dw:1371566911380:dw|
anonymous
  • anonymous
The domain is all values of y that are smaller than the \[y _{vertex}\] =4.75; y\[y \epsilon(-\infty, 4.75)\]
anonymous
  • anonymous
and range the x domain is \[x \epsilon (-\infty,+\infty) or the real axis \]

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