The factored form of the quadratic expression 2a^2 - 8a - 20 using the "Complete the Square" method is 2(a - 2)^2 - 28. This expression is in the form (a - h)^2 + k, where h = 2 and k = -28, representing a parabolic function with its vertex at the point (2, -28).
Start with the given quadratic expression: 2a^2 - 8a - 20.
Factor out the coefficient of a^2 from the a^2 and a terms. In this case, the coefficient is 2:
2(a^2 - 4a) - 20
To complete the square, take half of the coefficient of the a term, square it, and add it inside the parentheses. The coefficient of the a term is -4, so half of that is -2, and squaring it gives 4:
2(a^2 - 4a + 4) - 20 - 8
The added term inside the parentheses is 4, so we need to subtract 2 times 4 (which is 8) outside the parentheses to maintain the equality:
2(a^2 - 4a + 4) - 20 - 8
Factor the perfect square trinomial inside the parentheses:
2(a - 2)^2 - 28
Now the expression is in the form (a - h)^2 + k, where h = 2 and k = -28. So, the factored form of the quadratic expression 2a^2 - 8a - 20 is: 2(a - 2)^2 - 28