CPhill

Your nose.......

x^2 - 9x + 24 = 0  

This has no x intercepts.....the discrminant =  b^2 - 4ac =  (-9)^2  - 4(1)(24)   =  81 - 96   = - 15

Anytime the discriminant < 0.......we won't have any real roots [ x intercepts]

Here's a graph to help you......https://www.desmos.com/calculator/esjonexqaa

Thanks....yes the world could  use more people like me......as for Melody???......that's debatable.....

LOL!!!!   [  don't tell her I said that.....!!!  ]

a.  I'm assuming this is  sqrt(x  - 2)....If so.......remember that the quantity under the sqare root can't be less than 0

So.....the minimum value for x  is 2........so the domain is  [2, infinity]

The range = [0, infinity ]

Restrictions  .....x cannot be less that 2

This function increases from   x = 2  to infinity

x= 2  makes this function 0.....therefore......it's a root

This function has no y intercept because it is not defined at x = 0

There are no "vertices"

Here's the graph......https://www.desmos.com/calculator/uu9oiez9ee

Here's something that might help on your essay....

http://www.history.com/topics/american-civil-war/shermans-march

OK......I'll see if I can help......

Thanks, guest.....the reason for  Guest's answer is that......

slope =   [ change in y's ] / [ change in x's ]   

But....on a horizontal line, the y values are constant, so there is no change in them......only the x values change......

Another more intuitive explanation is that a horizontal line neither "rises" nor "falls."......Thus, it's "slope"  =  0

Go ahead......

The side of the square  = sqrt(50)m

The diagonal of any sqare =  sqrt(2)  * tthe side length

I'll let you take it from there, saseflower...!!!!

Go with Melody's  answer.....mine sucks.....!!!!