If you horizontally stretch the quadratic parent function f (x) = x^2 by a factor of 4 what's the equation of the new function

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.