anonymous
  • anonymous
Find the equation of a quadratic function f whose graph has a vertical axis of symmetry x = -2, the range of f is given by the interval [4 , +infinity) and f(2) = 8.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you are being told in a round about way that the vertex is \((-2,4)\)
anonymous
  • anonymous
this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)
anonymous
  • anonymous
but you can solve for it, since \[f(2)=8\]you know \(8=a(2+2)^2+4\) and so \[16a+4=8\] \[16a=4\] \[a=\frac{1}{2}\]

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anonymous
  • anonymous
how come the vertex is (-2,4)? what does the vertical axis of symmetry x= -2 mean?
anonymous
  • anonymous
|dw:1353124009816:dw|
anonymous
  • anonymous
means a) the parabola is symmetric about the line \(x=-2\) and b) the first coordinate of the vertex is \(-2\)
anonymous
  • anonymous
the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)
anonymous
  • anonymous
I see...that's what I don't know before. I just know that there is a line x=-2
anonymous
  • anonymous
|dw:1353124262023:dw| if I may ask more, if the graph's like this, how would you say it in words?
anonymous
  • anonymous
yes but you can see it from the picture right? vertex is right on the axis of symmetry, so if it is \(x=-2\) then so is the first coordinate of the vertex
anonymous
  • anonymous
in your second example the parabola opens to the right, so the vertex would be a horizontal line, not a vertical one it would be something like \(y=2\)
anonymous
  • anonymous
sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense
anonymous
  • anonymous
how about the vertex for my second example? is it something like..(-2,0)?
anonymous
  • anonymous
anyway, big thanks for ur help @satellite73
anonymous
  • anonymous
I mean, if the axis of symmetry is y=2, then the vertex would be (-2,2), is this right?

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