Question

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

Answer 1

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

Answer 2

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

Answer 3

at least that is what i think it means

Answer 4

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

Answer 5

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

Answer 6

to finish, set
\[\frac{x^2}{2}=72\] and solve for \(x\)

Answer 7

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

Answer 8

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

Answer 9

yes please point out the mistakes

Answer 10

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

Answer 11

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

Answer 12

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"

Answer 13

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

Answer 14

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

Answer 15

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.

Answer 16

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

Answer 17

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

Answer 18

of course, if i am here

Answer 19

thanks

Answer 20

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