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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.1
you are being told in a round about way that the vertex is \((2,4)\)
 one year ago

satellite73Best 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 \(a\)
 one year ago

satellite73Best 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 \[16a+4=8\] \[16a=4\] \[a=\frac{1}{2}\]
 one year ago

candyfloss94Best 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?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
dw:1353124009816:dw
 one year ago

satellite73Best 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 \(2\)
 one year ago

satellite73Best 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 \(4\)
 one year ago

candyfloss94Best 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
 one year ago

candyfloss94Best 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?
 one year ago

satellite73Best 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
 one year ago

satellite73Best 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 \(y=2\)
 one year ago

satellite73Best 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
 one year ago

candyfloss94Best ResponseYou've already chosen the best response.0
how about the vertex for my second example? is it something like..(2,0)?
 one year ago

candyfloss94Best ResponseYou've already chosen the best response.0
anyway, big thanks for ur help @satellite73
 one year ago

candyfloss94Best 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?
 one year ago
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