## candyfloss94 2 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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1. satellite73

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

2. satellite73

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

3. satellite73

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

4. candyfloss94

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

5. satellite73

|dw:1353124009816:dw|

6. satellite73

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

7. satellite73

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

8. candyfloss94

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

9. candyfloss94

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

10. satellite73

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

11. satellite73

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 $$y=2$$

12. satellite73

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

13. candyfloss94

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

14. candyfloss94

anyway, big thanks for ur help @satellite73

15. candyfloss94

I mean, if the axis of symmetry is y=2, then the vertex would be (-2,2), is this right?