Question

If F(x) 2x2 - 4x, find F(5 + c). Enter the expression in simplest form.

Answer 1

To find F(5 + c) for F(x) = 2x^2 - 4x, substitute (5 + c) into the function and simplify to get the result 2c^2 + 16c + 30.

Step-by-step explanation:

The question asks to find F(5 + c) given the function F(x) = 2x2 - 4x. To do this, you substitute (5 + c) in place of x in the function. Here are the steps:

1. Start with the original function F(x) = 2x2 - 4x.
2. Replace every instance of x with (5 + c), which gives F(5 + c) = 2(5 + c)2 - 4(5 + c).
3. Expand the square: (5 + c)2 = 52 + 2 × 5 × c + c2 = 25 + 10c + c2.
4. Substitute back into the function: F(5 + c) = 2(25 + 10c + c2) - 4(5 + c) = 50 + 20c + 2c2 - 20 - 4c.
5. Combine like terms: F(5 + c) = 2c2 + 16c + 30.

So, the simplified form of F(5 + c) is 2c2 + 16c + 30.