Final answer:
The expression that represents f(x + 2) is 2x² + 8x + 5, obtained by substituting x + 2 into the original function f(x) = 2x² - 3 and simplifying.
Step-by-step explanation:
To find the expression that represents f(x + 2), we need to substitute x + 2 into the original function f(x) = 2x2 - 3. This gives us:
f(x + 2) = 2(x + 2)2 - 3
Expanding the squared term yields:
f(x + 2) = 2(x2 + 4x + 4) - 3
And then distributing the 2:
f(x + 2) = 2x2 + 8x + 8 - 3
Simplify by combining like terms:
f(x + 2) = 2x2 + 8x + 5
Therefore, the expression that represents f(x + 2) is 2x2 + 8x + 5.