Evaluate f(a+h)-f(a) for the quadratic function f(x)=x^2+2

Answer 1

From the question, we have f(x) = x^2 + 2.

If the question is asking f(a+h), it means plugging x = a+h into the equation (wherever you find x, just replace it with (a+h)

Therefore, f(a+h) + f(a) = (a+h)^2 + 2 - ( a^2 + 2) = a^2 + 2ah + h^2 + 2 - a^2 - 2 = h^2 + 2ah

Answer 2

Lets first write out what each of these things are. If f(x) = x² + 2, then f(a) = a² + 2, and f(a+h) = (a+h)² + 2.

Now lets do the subtraction: f(a+h) - f(a) = (a+h)² + 2 - (a² + 2) = a² + 2ah + h² + 2 - a² - 2 =

2ah + h².

Answer 3

Let f(x) = x² + 2.

Find f(a) and f(a + h).

f(a) = a² + 2

f(a + h) = (a + h)² + 2 = a² + 2ah + h² + 2

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