f(x)=5x^2+4x-5

Question

a.) f(a+2)       b.)  f(a+h)-f(a)

Answer 1

a.) In order to get f(a+2), substitute a+2 for x in the original equation for the function:

f(a+2) = 5(a+2)²+4(a+2) - 5 = 5(a²+4a+4) + 4a + 8 - 5 = 5a² + 20a + 20 + 4a + 3 = 5a² + 24a + 23

 

b.) In order to get f(a+h) substitute a+h for x in the original eqaution:

 

f(a+h) = 5(a+h)²+4(a+h) - 5 = 5(a²+2ah+h²) + 4a + 4h - 5 = 5a² + 10ah + 5h² + 4a + 4h-5 

f(a) = 5a² + 4a - 5

 

Then f(a+h) - f(a) = 5a² + 10ah + 5h² + 4a + 4h-5 - (5a² + 4a - 5) = 10ah + 5h² + 4h