## anonymous one year ago question 1) You have decided to buy 3 pieces of lumber to make a raised bed. You will cut one of the pieces in half to make two ends of the bed. Write a function for the area of this plot in terms of the length of the lumber you purchased. Use your graphing calculator or graph paper to graph the function. Name the vertex of the parabola. Name the axis of symmetry. Describe how the graph of this function is related to the parent function, y = x2. How long must each piece of lumber be before cutting in order to have a garden with an area of 75 ft2? Explain your method.Show work

1. misty1212

i guess you are supposed to give a variable to the length of one piece of lumber probably $$x$$ = length

2. misty1212

then if you cut one in half, its length will be $$\frac{x}{2}$$ and the area will be $A(x)=x\times \frac{x}{2}=\frac{x^2}{2}$

3. misty1212

at least that is what i think it means

4. misty1212

picture looks like this http://www.wolframalpha.com/input/?i=x%5E2%2F2

5. misty1212

vertex is $$(0,0)$$ and axis of symmetry is $$x=0$$ aka the $$y$$ axis

6. misty1212

to finish, set $\frac{x^2}{2}=72$ and solve for $$x$$

7. misty1212

oh no i guess $\frac{x^2}{2}=75$ which is somewhat harder

8. misty1212

now, would you like me to point out the mistake in this math teacher question?

9. anonymous

yes please point out the mistakes

10. misty1212

the mistake is that for this function to make sense, you are buying lumber since you certainly cannot buy a negative amount of lumber, nor can you make a raised bed with 0 feet of lumber, the function only makes sense if $$x>0$$ or as they say "the domain is $$x>0$$ the function should not exist on the left side of the y axis

11. misty1212

which means the graph actually looks like this http://www.wolframalpha.com/input/?i=x%5E2%2F2+domain+0..10

12. misty1212

therefor it is not a parabola, it is only a half of a parabola and so it has no "axis of symmetry" and no "vertex"

13. misty1212

state of math education continues to get worse unfortunately, it is not your fault, it is the math teachers they hire

14. misty1212

you have an actual teacher or is this some sort of FLVS silliness?

15. anonymous

I am in an online high school. It is so awful, the teachers literally take days to reply to my questions sometimes it's so frustrating. Thank you so much for your help.

16. misty1212

$\color\magenta\heartsuit$ btw feel free to copy and paste what i wrote about how this question is dumb and send it to them

17. anonymous

Ok, I will do that, Would be willing to help me in the future when I need help ?

18. misty1212

of course, if i am here

19. anonymous

thanks

20. anonymous

would you mind telling me how I can type in math symbols on my laptop for example 2spuared or a fraction.