Write the function in standard form

Question

The equation that is being solved is f(x)=2^2x-8x-3

 

written in f(x)=a(x-h)^2+k

Answer 1

This question has already been answered. Here's the solution again.
I think the equation should be f(x)=2x^2-8x-3. We can write this: 2(x^2-4x)-3. The expression in parentheses needs to be converted to a perfect square. We do this by halving the coefficient of the x term and then squaring it. (4/2)^2=4, so the expression becomes x^2-4x+4=(x-2)^2. But we have to adjust -3 to compensate for the number we just added. 2(x-2)^2=2x^2-8x+8 so we need to subtract the 8 we added and combine it with -3 making it -11. So f(x)=2(x-2)^2-11, the standard parabolic form. Quick check: when x=0, f(x)=-3.