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anonymous
 3 years ago
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.
anonymous
 3 years ago
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.

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you are being told in a round about way that the vertex is \((2,4)\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but you can solve for it, since \[f(2)=8\]you know \(8=a(2+2)^2+4\) and so \[16a+4=8\] \[16a=4\] \[a=\frac{1}{2}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0how come the vertex is (2,4)? what does the vertical axis of symmetry x= 2 mean?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1353124009816:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0means a) the parabola is symmetric about the line \(x=2\) and b) the first coordinate of the vertex is \(2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I see...that's what I don't know before. I just know that there is a line x=2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1353124262023:dw if I may ask more, if the graph's like this, how would you say it in words?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes 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
 3 years ago
Best ResponseYou've already chosen the best response.0in 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
 3 years ago
Best ResponseYou've already chosen the best response.0sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0how about the vertex for my second example? is it something like..(2,0)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0anyway, big thanks for ur help @satellite73

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I mean, if the axis of symmetry is y=2, then the vertex would be (2,2), is this right?
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