Question

Completing the square for the given standard form of the quadratic equation, y = x^2 - 10x + 25, and obtain the vertex (h, k) from the vertex form of the quadratic equation (y = a(x - h)^2 + k).

Answer 1

The given quadratic equation is a perfect square and can be written in vertex form as y = (x - 5)^2, revealing the vertex to be (5, 0).

Step-by-step explanation:

Completing the square for the quadratic equation y = x^2 - 10x + 25 is actually quite straightforward in this case, because the equation already represents a perfect square. The equation can be rewritten in the vertex form y = a(x - h)^2 + k where a is the coefficient of the x^2 term, and (h, k) is the vertex of the parabola. Here, a = 1, and the trinomial x^2 - 10x + 25 can be factored to (x - 5)^2. Thus, the equation in vertex form is y = (x - 5)^2 with a vertex at (5, 0).