Question

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

Answer 1

g(x) = ¹/₁₆x²

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.