To rewrite the quadratic function f(x) = x² – 6x + 2 in vertex form, we will use the completing the square method.
First, we’ll focus on the x² and -6x part of the equation:
x² – 6x
Next, we need to complete the square. To do this, take half of the coefficient of x (which is -6), square it, and add it inside the parentheses:
Half of -6 is -3. Squaring -3 gives us 9. So, we rewrite:
x² – 6x = (x – 3)² – 9
Now, we can rewrite the original function:
f(x) = (x – 3)² – 9 + 2
Combine the constants -9 and +2:
f(x) = (x – 3)² – 7
This results in the vertex form of the function. The vertex form is generally written as f(x) = a(x – h)² + k, where (h, k) is the vertex of the parabola. In this case, the vertex is at (3, -7).
Thus, the final answer is:
f(x) = (x – 3)² – 7