Question

If f(n) = 4n^2 - 5, what is the value of f(a+3) in standard form?

Answer 1

The value of f(a+3) is found by substituting a+3 into the function f(n) = 4n^2 - 5, squaring the expression, and simplifying to get the result 4a^2 + 24a + 31 in standard form.

Step-by-step explanation:

To find the value of f(a+3) when f(n) = 4n2 - 5, you follow these steps:

1. Substitute a + 3 in place of n in the function f(n).
2. Apply the squared operation: (a + 3)2 = a2 + 6a + 9.
3. Multiply the result by 4 and then subtract 5 according to the function's rule: 4(a2 + 6a + 9) - 5.
4. Simplify the expression: 4a2 + 24a + 36 - 5, which simplifies to 4a2 + 24a + 31.

So the value of f(a+3) in standard form is 4a2 + 24a + 31.