Sat 2015 Practice Test #1 Answer Explanations

Choice D is correct.
Any quadratic function 
T
can be written in the 
form 
T
(
[
) = 
D
(
[ơ
h
)
2
+ 
k
, where 
D
, 
h
, and 
k
are constants and (
h
, 
k
) 
is the vertex of the parabola when 
T
is graphed in the coordinate 
plane. This form can be reached by completing the square in the 
H[SUHVVLRQWKDWGHƮQHVT
. The equation of the graph is 
y
= 
[
2
ơ[ơ

---

_ 
_ 
6LQFHWKHFRHƱFLHQWRI[LVơWKLVHTXDWLRQFDQEHZULWWHQLQWHUPVRI
(
[ơ
2
= 
[
2
ơ[
+ 1 as follows: 
y
= 
[
2
ơ[ơ
[
2
ơ[ơ 
(
[ơ
2
ơ)URPWKLVIRUPRIWKHHTXDWLRQWKHFRHƱFLHQWVRIWKH
YHUWH[FDQEHUHDGDVơ
Choices A and C are incorrect because the coordinates of the vertex 
$
do not appear as constants in these equations. Choice B is incorrect 
because it is not equivalent to the given equation. 
QUESTION 31 
The correct answer is any number between 4 and 6, inclusive.
Since 
Wyatt can husk at least 12 dozen ears of corn per hour, it will take him 
_
no more than 72 
12
KRXUVWRKXVNGR]HQHDUVRIFRUQ2QWKHRWKHU
hand, since Wyatt can husk at most 18 dozen ears of corn per hour, 
_
it will take him at least 72 
18 = 4 hours to husk 72 dozen ears of corn. 
Therefore, the possible times it could take Wyatt to husk 72 dozen ears 
of corn are 4 hours to 6 hours, inclusive. Any number between 4 and 6, 
inclusive, can be gridded as the correct answer. 
QUESTION 32