Question

look at this graph: what are the coordinates of the vertex? ( , )

Explanation:

Step1: Recall the definition of the vertex of a parabola

The vertex of a parabola is the point where the parabola changes direction. For a parabola \(y = ax^{2}+bx + c\), the \(x\) - coordinate of the vertex is given by \(x=-\frac{b}{2a}\). In the case of the graph \(y = x^{2}\) (which is a basic parabola), \(a = 1\), \(b=0\), so \(x = 0\).

Step2: Find the \(y\) - coordinate

Substitute \(x = 0\) into the equation \(y=x^{2}\). Then \(y=(0)^{2}=0\).

Answer:

\((0,0)\)