If f(x) = x^2 + 3x - 6, then f(x+2)=? a. x^2 + 1 b. x^2 + x + 1 c. x^2 + x + 10 d. x^2 + 7x + 4 e. x^2 + 7x + 12

D: x^2 + 7x + 4

Explanation:

To solve this, we have to replace the x in the equation to x + 2.

f(x+2) = (x+2)^2 + 3(x+2) - 6

Now we multiply the parenthesis with the number next to it.

f(x+2) = x^2 + 4x + 4 + 3x + 6 - 6

For the (x+2)^2, it becomes (x+2)(x+2), and in order to multiply them, use FOIL (First, Inner, Outer, Last). First, we multiply the first two numbers (x and x) to get x^2. Then, we multiply the inner and outer numbers (x * 2 and x * 2) to get 2x and 2x. then, we add those together to get 4x. After that, you multiply the last two numbers (2 and 2) to get four! So: (x+2)(x+2) = x^2 + 4x + 4!

Finally, you can simplify the numbers first by adding / subtracting similar numbers (numbers with the same exponent)

f(x+2) = x^2 + 7x + 4

Your answer is D!