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.

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

but you can solve for it, since 
$$f(2)=8$$you know $8=a(2+2)^2+4$ and so 
$$16a+4=8$$
$$16a=4$$
$$a=\frac{1}{2}$$

anonymous · Answer

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

anonymous · Answer

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anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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