Question

If the function f(x)=x²-12x+40 is converted to the form (x-b)b²+c and resulting equation is (x-6)²+c, what is the value of the constant c?

Answer 1

The value of the constant c when the function f(x) = x² - 12x + 40 is expressed in the form (x-b)² + c is 4, which is found by completing the square method.

Step-by-step explanation:

The student is asking to find the value of the constant c when the quadratic function f(x) = x² - 12x + 40 is expressed in the form (x-b)² + c. To do this, we need to complete the square:

1. Start by identifying a, b, and c in the quadratic function, where a is the coefficient of x², b is the coefficient of x, and c is the constant term.
2. In the given function, a = 1, b = -12, and c = 40.
3. Complete the square by taking half of b, which is -6, and squaring it to get 36.
4. Rewrite the function as (x-(-6))² + (40 - 36), which simplifies to (x-6)² + 4.

So, the value of the constant c in the resulting equation (x-6)² + c is 4.