1)Jorge recorded the number of customers
y
that came to his store over a number
of hours
x. Does the data represent a

x
1 3 5 7 9

y
2 5 11 17 23

2) NASA has a plane that travels in a
parabola to simulate zero-gravity. Its
path can be modeled by the equation
y
8.6 x 2  560x  24000 where y is
the altitude in feet and
x is the time
since it started the maneuver. What is

a reasonable domain for this function?

No; the second differences

2. If they represented a quadratic function, we'd be able to find coefficients a,b,c such that all pairs (x,y) from your table satisfy $\displaystyle y=ax^2+bx+c$.

Pair (1,2) gives $\displaystyle 2=a+b+c$$\displaystyle \; \displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;(1) Pair (3,5) gives \displaystyle 5=9a+3b+c$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$ (2)
Pair (5,11) gives $\displaystyle 11=25a+5b+c$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \; (3) Pair (7,17) gives \displaystyle 17=49a+7b+c$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$$\displaystyle \;$ (4)

Subtracting (1) from (2) we get $\displaystyle 3=8a+2b$ $\displaystyle \;$ $\displaystyle \;$ $\displaystyle \;$ $\displaystyle \;$(5)
Subtracting (2) from (3) we get $\displaystyle 6=16a+2b$$\displaystyle \; \displaystyle \; \displaystyle \; \displaystyle \;(6) Subtracting (3) from (4) we get \displaystyle 6=24a+2b$$\displaystyle \;$ $\displaystyle \;$ $\displaystyle \;$ $\displaystyle \;$(7)

Subtracting (5) form (6) we get $\displaystyle 3=8a$
Subtracting (6) form (7) we get $\displaystyle 0=8a$

This means there's no solution, so the data can't be represented by a quadratic function.

The second part is illegible for me.

3. Originally Posted by sri340

...
a plane that travels in a

parabola to simulate zero-gravity. Its
path can be modeled by the equation

y 8.6 x 2  560x  24000 where y is
the altitude in feet and x is the time

since it started the maneuver. What is

a reasonable domain for this function?
I cannot understand what the boxes are supposed to be:
is this the equation:

$\displaystyle y = -8.6 x^2 + 560x + 24000$

Just to make sure, is the time supposed to be in seconds?