I need help on this math question please I really need help

Question

The function P(x) is mapped to I(x) by a dilation in the following graph. 

 Which answer gives the correct transformation of P(x) to get to I(x)?

I(x)=1/2P(x)

I(x)=P(2x)

I(x)=P(1/2x)

I(x)=2P(x)

Answer 1

last option: f(x) = 2P(x)

I(x) = y = .16x^2 -2

P(x) = y = .08x^2 -2

P(x) = (1/2)I(x)

I(x) = 2P(x)

the transformation from P to I is a vertical stretch, by a factor of 2

also the vertex decreases by 6, vertical decrease by 6

x coordinate of the vertex remains the same, x= 2