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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
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you are being told in a round about way that the vertex is \((-2,4)\)
this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)
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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Other answers:

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

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