Question

For the function f(x)=4x^2+6x−1, evaluate f(a+h).

a) 4(a^2+2ah+h^2) + 6a +6h-1
b) 4a^2 + 8ah + 6a + 4h^2 + 6h-1
c) 4a^2+6a+2ah+h^2 + 6a +6h-1
d) 4(a^2+2h^2) + 6a +8ah-1

Answer 1

To evaluate f(a + h) for the function f(x) = 4x^2 + 6x - 1, we substitute (a + h) for x, expand, and simplify to get 4a^2 + 8ah + 4h^2 + 6a + 6h - 1, which is answer choice b).

Step-by-step explanation:

To evaluate the function f(x) = 4x^2 + 6x - 1 for f(a + h), we substitute (a + h) in place of x and expand the expression.

Starting with f(a + h) = 4(a + h)^2 + 6(a + h) - 1, we first expand the square:

(a + h)^2 = a^2 + 2ah + h^2

Substitute this into the function:

4(a^2 + 2ah + h^2) + 6(a + h) - 1

Multiplying through the terms, we get:

4a^2 + 8ah + 4h^2 + 6a + 6h - 1

This corresponds to answer choice b).