Answer:
g(x) = ¹/₁₆x²
Step-by-step explanation:
The parent function is ƒ(x) = x².
Then g(x) = (ax)² is either a compression or a stretch of the parent function .
0 < |a| < 1 is a stretch by a factor of 1/a.
Thus, if you want to stretch a parabola by a factor of 4
,
a = ¼
and the equation of the new function is
g(x) = (¼x)² or
g(x) = ¹/₁₆x²
The diagram below shows that
ƒ(x) = 1 when x = 1 but
g(x) = 1 when x =4
The parabola has been stretched by a factor of 4.
