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.