Complete the square to rewrite the function f(x)=3x2–12x+5 in the form f(x)=a(x–h)2+k.

Sure, here are the steps to complete the square for the function f(x)=3x²–12x+5:

1. First, we need to factor out the coefficient of x² from the first two terms. This gives us f(x) = 3(x² - 4x) + 5.

2. Next, we need to complete the square inside the parentheses. To do this, we take half of the coefficient of x, square it, and add and subtract it inside the parentheses. Half of -4 is -2, and -2² = 4. So, we get f(x) = 3[(x² - 4x + 4) - 4] + 5.

3. Simplify the equation inside the parentheses to get a perfect square trinomial. This gives us f(x) = 3[(x - 2)² - 4] + 5.

4. Distribute the 3 into the parentheses and simplify to get f(x) = 3(x - 2)² - 12 + 5.

5. Finally, simplify the constants to get the function in vertex form: f(x) = 3(x - 2)² - 7.

So, the function f(x)=3x²–12x+5 in the form f(x)=a(x–h)²+k is f(x) = 3(x - 2)² - 7.