Question

PLEASE HELP!! TIMED QUESTION!!!!!

If f(x) = x^2 + 3x + 5 , what is f (a + h) ?


A. (a+h)^2 + 3(a+h) + 5(a+h)

B. a^2 + 2ah + h^2 + 3a + 3h + 5

C. h^2 + 3a + 3h + 5

D. (x^2 + 3ax + 5) (a + h)

Answer 1

`\large\boxed{B.\ a^2+2ah+h^2+3a+3h+5}`

Explanation:

`f(x)=x^2+3x+5\\\\f(a+h)\to\text{substitute}\ x=a+h\ \text{to the equation:}\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{Use}\ (x+y)^2=x^2+2xy+y^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5`