i need some help with this pleez!

f(x+6)

f(x)=3x^2-5x+3

if u could explain in steps that would be great! :)

If f(x) = 3x^2-5x+3, then
f(x+6) = 3(x+6)^2 + 5(x+6) + 3

Multiply that out and combine terms.

To find f(x+6), you need to substitute (x+6) into the original function f(x).

Step 1: Replace x with (x+6) in f(x)=3x^2-5x+3.
f(x+6) = 3(x+6)^2 - 5(x+6) + 3.

Step 2: Simplify the expression inside the parentheses.
f(x+6) = 3(x^2 + 12x + 36) - 5(x+6) + 3.

Step 3: Expand the binomial square and distribute the coefficients.
f(x+6) = 3x^2 + 36x + 108 - 5x - 30 + 3.

Step 4: Combine the like terms.
f(x+6) = 3x^2 + (36x - 5x) + (108 - 30 + 3).

Step 5: Simplify further.
f(x+6) = 3x^2 + 31x + 81.

Therefore, f(x+6) = 3x^2 + 31x + 81.