Question

the roots of f(x)=0 are 0 and 1. what are the roots of f(2x)?

Answer 1

the roots of f(2x) will be 1/2 of the roots of f(x), because:

\[f(2*\frac{0}{2}) = f(0) = 0, f(2*\frac{1}{2}) = f(1) = 0\]

so the roots of f(2x) = 0 and 1/2

Answer 2

lol i was thinking cause 2x means graph horizontally compressed by 1/2 thats why is that same reason?

Answer 3

yes, that reasoning also works. Another way is also to create the quadratic equation itself.

Answer 4

umm we dont know a value can we still do it?

Answer 5

like vertical stretch

Answer 6

if the roots are 0 and 1, the quadratic equation is:

\[x^2-x\] plugging in 2x gives:
\[(2x)^2-(2x) = 4x^2-2x = 2x(2x-1)\]

Answer 7

ah i c

Answer 8

i prefer the way I did it up top and your reasoning to that method though. Less work lol

Answer 9

lol thnkx