## 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. one year ago one year ago

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1. satellite73 Group Title

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

2. satellite73 Group Title

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

3. satellite73 Group Title

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 Group Title

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

5. satellite73 Group Title

|dw:1353124009816:dw|

6. satellite73 Group Title

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

7. satellite73 Group Title

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

8. candyfloss94 Group Title

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

9. candyfloss94 Group Title

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

10. satellite73 Group Title

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 Group Title

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 Group Title

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

13. candyfloss94 Group Title

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

14. candyfloss94 Group Title

anyway, big thanks for ur help @satellite73

15. candyfloss94 Group Title

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