Final answer:
To rewrite the function by completing the square, transform f(x) = x² - 12x + 50 into (x - 6)² + 14. Take half of the x term's coefficient, square it, add and subtract it inside the equation, and rearrange to form a perfect square trinomial.
Step-by-step explanation:
To rewrite the function by completing the square, we start with the given quadratic function f(x) = x² - 12x + 50. Completing the square involves creating a perfect square trinomial from the quadratic equation. We will transform the f(x) into the form (x - h)² + k where h and k are constants.
First, we look at the coefficient of the x term, which is -12, and take half of it, getting -6. Then, we square this number to get 36. We add and subtract this square inside the equation to maintain equality:
f(x) = x² - 12x + 36 - 36 + 50
The first three terms now form a perfect square trinomial, and we can rewrite f(x) as:
f(x) = (x - 6)² + 14
We have now successfully rewritten the quadratic function by completing the square. The function is in a form that makes it easier to graph and to identify the vertex of the parabola, which is at (6, 14).