Melody

9C0×7C5 + 9C1×7C4 + 9C2×7C3

I'm on a phone and it is too difficult to go futher but you can finish it  :) 

Nice one Chris!

Here is the graph.

Thanks Chris :)

24C10      This is where order does not count    (combinations)

$${\left({\frac{{\mathtt{24}}{!}}{{\mathtt{10}}{!}{\mathtt{\,\times\,}}({\mathtt{24}}{\mathtt{\,-\,}}{\mathtt{10}}){!}}}\right)} = {\mathtt{1\,961\,256}}$$

24P10      This is where order does count     (permutations)

$${\left({\frac{{\mathtt{24}}{!}}{({\mathtt{24}}{\mathtt{\,-\,}}{\mathtt{10}}){!}}}\right)} = {\mathtt{7\,117\,005\,772\,800}}$$

$$\\y=2(x+4)(x-2p) \qquad p\in R\\
$This is a concave up parabola$\\
$Roots are $ x=-4 \;\;and\;\;x=2p\\
$Axis of symmetry is $ x=(2p+-4)/2 = p-2\\
Min:\\
y=2(p-2+4)(p-2-2p)\\
y=2(p+2)(-2-p)\\
y=-2(p+2)^2\\
$You want this value to be $-18\\
-18=-2(p+2)^2\\
9=(p+2)^2\\
p+2=\pm3\\
p=\pm3-2\\
p=1 \quad or \quad p=-5$$

Because 

$$\\sin\;x^2+10\\
means \\(sin(x^2))+10\\
$If you want the sine of $ (x^2+10)\\
$then it should be written as $
sin(x^2+10)$$

that is better.

y=|7-x|

when x=0

y=|7-0|=|7|=7

(0,7)

i am a little confused as to what you are having trouble with,   

Perhaps this is what you want?

-------------------

If 7-x> 0 then y=7-x

this rearranges to If x<7  then y=-x+7

----------------------

If 7-x<0 then y=-7+x

this rearranges to 

If x>7 then  y=x-7

------------------------

does that help?

I cannot see the picture and I have no idea what you are talking about.   LOL