Question

Ashley graphs two quadratic functions,
f
(
x
)
=
x
2
+
4
x
+
1
, and
g
(
x
)
=
3
f
(
x
)
, in the same coordinate plane.



Which statement BEST explains the graphs of
f
(
x
)
and
g
(
x
)
?



A.
Graph:
g
(
x
)
is wider than
f
(
x
)

y
-intercept:
g
(
x
)
is less than
f
(
x
)

B.
Graph:
g
(
x
)
is wider than
f
(
x
)

y
-intercept:
g
(
x
)
is greater than
f
(
x
)

C.
Graph:
g
(
x
)
is narrower than
f
(
x
)

y
-intercept:
g
(
x
)
is less than
f
(
x
)

D.
Graph:
g
(
x
)
is narrower than
f
(
x
)

y
-intercept:
g
(
x
)
is greater than
f
(
x
)

Answer 1

Answer: D.

Explanation: g(x) = 3f(x) = 3x^2 + 12x + 3 has leading coefficient 3 (vs 1 for f), so it's a vertical stretch by factor 3 and therefore "narrower" than f. The y-intercepts are f(0)=1 and g(0)=3, so g's y-intercept is greater than f's.