Question

Choose the equation that shows a step in the process of completing the square on the given quadratic. y = x2 + 8x – 3 y = x2 + 8x + 8 – 3 – 8 y = x2 + 8x + 8 – 3 + 8 y = x2 + 8x + 16 – 3 – 16 y = x2 + 8x + 16 – 3 + 16

Answer 1

Explanation:

The correct equation that shows a step in the process of completing the square on the given quadratic y = x^2 + 8x – 3 is y = x^2 + 8x + 16 – 3 – 16. Completing the square involves adding and subtracting a constant term in order to create a perfect square trinomial. In this case, the constant term added is (8/2)^2 = 16, which is half the coefficient of the x-term squared. This step transforms the quadratic into the form (x + a)^2 + b, where a represents half of the x-term coefficient and b represents the constant term.

By adding 16 to the equation to create a perfect square trinomial, we need to subtract 16 afterward to maintain the equation’s balance. Thus, the equation becomes:

y = x^2 + 8x + 16 - 3 - 16

Simplifying further:

y = (x + 4)^2 - 19

Therefore, the correct equation is:

y = (x + 4)^2 - 19