Help solve this calculus problem

Question

Let f(x)= 2x^2-6x+7.

^Find f(a+h) - f(a) divided by h

Answer 1

Let f(x)=2x²–6x+7. Find [f(a+h)–f(a)] / h.

First replace x in the given function with (a+h) to get f(a+h). Then replace x in the given function with (a) to get f(a). Then, rewrite the expression [f(a+h)–f(a)] / h as follows:

[ f(a+h) – f(a) ] / h

[ (2(a+h)²– 6(a+h)+7) – (2a²– 6a+7) ] / h. Now, let's simplify! Foil (a+h)² to get (a²+2ah+h²).

[ (2(a²+2ah+h²) – 6(a+h) + 7) – (2a²– 6a+7) ] / h. Distribute the 2, – 6, and – to get the following:

[ 2a²+4ah+2h²– 6a – 6h+7 – 2a²+6a –7 ] / h. Group like terms in descending order, alphabetically!

[ 2a²– 2a²+2h²+4ah–6a+6a–6h+7–7 ] / h. Then, combine like terms as shown below!

[ 2a²– 2a²+2h²+4ah –6a+6a –6h +7–7 ] / h. Now re-write your answer simplified.

[2h²+4ah–6h] / h. Divide by h to get your answer.

= 2h+4a–6. Rewrite in standard form or descending order, alphabetically.

= 4a+2h–6. Therefore, [f(a+h)–f(a)] / h = 4a+2h–6. Done!

Answer 2

f(a + h) = 2(a + h)² - 6(a + h) + 7

f(a + h) = 2(a² + 2ah + h²) - 6a - 6h + 7

f(a + h) = 2a² + 4ah + 2h² - 6a - 6h + 7

f(a) = 2a² - 6a + 7

f(a + h) - f(a) = 4ah + 2h² - 6h

[f(a + h) - f(a)] / h = 4a - 6 + 2h