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Svetllana [295]
3 years ago
15

Find and simplify the expression if f(x)=x^2-10. f(4+h)-f(4)=

Mathematics
2 answers:
11111nata11111 [884]3 years ago
8 0

f(4+h)-f(4)=(4+h)^2-10-(4^2-10)\\f(4+h)-f(4)=16+8h+h^2-10-16+10\\f(4+h)-f(4)=h^2+8h

sattari [20]3 years ago
3 0

Answer:

f (4 + h) -f (4) = h ^ 2 + 8h

Step-by-step explanation:

We have the following quadratic function.

f (x) = x ^ 2-10

We must find the following expression

f (4 + h) -f (4) =

First we must find f (4 + h)

Then substitute x = (4 + h) in the quadratic equation:

f (4 + h) = (4 + h) ^ 2 -10\\\\f (4 + h) = 16 + 8h + h ^ 2 -10\\\\f (4 + h) = h ^ 2 + 8h +6

Now we find f(4). Replace x = 4 in the function f (x)

f (4) = (4) ^ 2-10\\\\f (4) = 16-10\\\\f (4) = 6

Finally we have to:

f (4 + h) -f (4) = h ^ 2 + 8h +6 - 6

f (4 + h) -f (4) = h ^ 2 + 8h

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