Evaluate the function.
g(n) = -3n^2 + 2; Find g(n+3)
-3(n+3)^2+2
=-3(n^2+6n+9)+2
=-3n^2-18n-27+2
=3n^2-18n-25
(Use quadratic formula to solve for n)
for the last line, don't you mean -3n^2 and not just 3
Yeah it's -3n^2, sorry about that. :)
To find g(n+3), we need to substitute (n+3) into the equation for g(n). Here's how you can do it:
Step 1: Start with the original equation for g(n): g(n) = -3n^2 + 2.
Step 2: Substitute (n+3) for n in the equation: g(n+3) = -3(n+3)^2 + 2.
Step 3: Expand and simplify the equation. To expand (n+3)^2, you can use the FOIL method or the formula (a+b)^2 = a^2 + 2ab + b^2.
(n+3)^2 = n^2 + 2(3)(n) + 3^2
= n^2 + 6n + 9
Plugging this back into the equation, we get:
g(n+3) = -3(n^2 + 6n + 9) + 2
Step 4: Simplify further by distributing the -3:
g(n+3) = -3n^2 - 18n - 27 + 2
Step 5: Combine like terms:
g(n+3) = -3n^2 - 18n - 25
So, the function g(n+3) is -3n^2 - 18n - 25.