Question

30 POINTS! The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).

Answer 1

Hey there!!!

Equation given :

p ( x ) =  3x² + 4x + 5

Find p ( 2x )

In order to solve this, we will have to substitute the value 2x instead of x

Hence,

... p ( 2x ) = 3 ( 2x )² + 4 ( 2x ) + 5

... p ( 2x ) = 3 ( 8x² ) + 8x + 5

... p ( 2x ) = 24x² + 8x + 5

As we know I ( x ) = p ( 2x )

The value of  I(x) = 24x² + 8x + 5

Hope my answer helps!

Answer 2

Answer:

$P(2x)=12x^{2} +8x+5$

Step-by-step explanation:

To obtain the new function indicated by I (x) = P (2x), it means that we must substitute in the original equation every time we find "x", the value of "2x

So, for $P(x)=3x^{2}+4x+5$

replacing I(x)=P(2x)

$P(2x)=3(2x)^{2} +4(2x)+5$

performing indicated operations

$P(2x)=3(4x^{2} )+8x+5$

$P(2x)=12x^{2} +8x+5$