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- 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.

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- anonymous

- katieb

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- anonymous

you are being told in a round about way that the vertex is \((-2,4)\)

- anonymous

this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)

- 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

how come the vertex is (-2,4)? what does the vertical axis of symmetry x= -2 mean?

- anonymous

|dw:1353124009816:dw|

- anonymous

means
a) the parabola is symmetric about the line \(x=-2\) and
b) the first coordinate of the vertex is \(-2\)

- anonymous

the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)

- anonymous

I see...that's what I don't know before. I just know that there is a line x=-2

- anonymous

|dw:1353124262023:dw|
if I may ask more, if the graph's like this, how would you say it in words?

- 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

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

sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense

- anonymous

how about the vertex for my second example? is it something like..(-2,0)?

- anonymous

anyway, big thanks for ur help @satellite73

- 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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