identify the graph of y = x².

Explanation:

Step1: Recall properties of $y = x^{2}$

The function $y=x^{2}$ is a quadratic function. Its general form is $y = ax^{2}+bx + c$ where $a = 1$, $b=0$, $c = 0$. The graph of a quadratic function $y=ax^{2}+bx + c$ is a parabola. When $a>0$, the parabola opens upwards.

Step2: Analyze the vertex

For the quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is given by $x=-\frac{b}{2a}$. Since $b = 0$ and $a=1$, the x - coordinate of the vertex is $x = 0$. Substituting $x = 0$ into $y=x^{2}$, we get $y=0$. So the vertex is at the origin $(0,0)$.

Answer:

The third graph (the parabola that opens upwards with vertex at the origin).