Answer:
D: x^2 + 7x + 4
Step-by-step 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!