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candyfloss94
Group Title
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.
 2 years ago
 2 years ago
candyfloss94 Group Title
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.
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you are being told in a round about way that the vertex is \((2,4)\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
but you can solve for it, since \[f(2)=8\]you know \(8=a(2+2)^2+4\) and so \[16a+4=8\] \[16a=4\] \[a=\frac{1}{2}\]
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
how come the vertex is (2,4)? what does the vertical axis of symmetry x= 2 mean?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
dw:1353124009816:dw
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
means a) the parabola is symmetric about the line \(x=2\) and b) the first coordinate of the vertex is \(2\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
I see...that's what I don't know before. I just know that there is a line x=2
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
dw:1353124262023:dw if I may ask more, if the graph's like this, how would you say it in words?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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 \(y=2\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
how about the vertex for my second example? is it something like..(2,0)?
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
anyway, big thanks for ur help @satellite73
 2 years ago

candyfloss94 Group TitleBest ResponseYou've already chosen the best response.0
I mean, if the axis of symmetry is y=2, then the vertex would be (2,2), is this right?
 2 years ago
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