Question: User: graph $x^2$
1. The problem is to graph the function $y = x^2$.
2. This is a quadratic function, which forms a parabola opening upwards.
3. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$.
4. Important features include the vertex at $(0,0)$, the axis of symmetry $x=0$, and the parabola opening upwards because $a>0$.
5. To plot, calculate some points:
- When $x=-2$, $y=(-2)^2=4$.
- When $x=-1$, $y=(-1)^2=1$.
- When $x=0$, $y=0^2=0$.
- When $x=1$, $y=1^2=1$.
- When $x=2$, $y=2^2=4$.
6. Plot these points and draw a smooth curve through them to form the parabola.
Final answer: The graph of $y = x^2$ is a parabola with vertex at the origin and symmetric about the y-axis.