Given f(x)=-10x2-42x-17
find f(x+h)
Substitute x with x + h.
f(x + h) = -10(x + h)^2 - 42(x + h) - 17
Expand and simplify.
To find f(x+h), we need to substitute (x+h) for x in the equation f(x) = -10x^2 - 42x - 17.
Substitute (x+h) for x:
f(x+h) = -10(x+h)^2 - 42(x+h) - 17
Now we can expand and simplify the equation from here.
Step 1: Expand (x+h)^2
(x+h)^2 = (x+h)(x+h) = x(x+h) + h(x+h) = x^2 + 2xh + h^2
Step 2: Substitute the expanded form into the equation:
f(x+h) = -10(x^2 + 2xh + h^2) - 42(x+h) - 17
Step 3: Distribute the -10 and -42
f(x+h) = -10x^2 - 20xh - 10h^2 - 42x - 42h - 17
And that is the equation for f(x+h).