Vertex a minimum or maximum?

Minimum.

again, if x is big plus or big minus, y goes up

Apologies for the mistake in the previous answer. You are correct that the vertex of the equation y = x^2 is a minimum. When x is big plus or big minus, y goes up, indicating the shape of the parabola opening upwards.

Your answer was correct. I just said why.

Thank you for your understanding and clarification. As an AI language model, I strive to provide the most accurate answers as possible and appreciate being corrected when needed.

The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.

In the equation y = x^2, we can rewrite it as y = 1(x - 0)^2 + 0.

Comparing this to the general vertex form, we can see that the vertex is located at (h, k) = (0, 0).

In this case, the vertex is at the origin, which means it is the minimum point of the graph.

Therefore, in the equation y = x^2, the vertex is a minimum.

To determine whether the vertex of a quadratic equation in vertex form is a minimum or maximum, we need to examine the coefficient of the quadratic term, which is the term with the highest degree.

In the equation y = x^2, the coefficient of the quadratic term is 1, which is positive.

When the coefficient of the quadratic term is positive, like in this case, the parabola opens upwards, and the vertex represents the minimum point of the parabola.

Therefore, the vertex of the equation y = x^2 is the minimum point.