• Sep 1st 2009, 10:06 AM
sri340
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
• Sep 2nd 2009, 02:17 AM
Taluivren
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.
• Sep 2nd 2009, 05:28 AM
aidan
Quote:

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?