1. The problem is to graph the function $y = x^2$, which is a quadratic function. 2. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$. 3. Important rules for graphing quadratics: - The graph is a parabola. - If $a > 0$, the parabola opens upwards. - The vertex is at the point $(h, k)$ where $h = -\frac{b}{2a}$ and $k = c - \frac{b^2}{4a}$. - For $y = x^2$, the vertex is at $(0,0)$. 4. To graph $y = x^2$: - Plot the vertex at $(0,0)$. - Choose values of $x$ (e.g., $-2, -1, 0, 1, 2$). - Calculate corresponding $y$ values: $y = (-2)^2 = 4$, $y = (-1)^2 = 1$, $y = 0^2 = 0$, $y = 1^2 = 1$, $y = 2^2 = 4$. - Plot these points: $(-2,4)$, $(-1,1)$, $(0,0)$, $(1,1)$, $(2,4)$. - Draw a smooth curve through these points forming a symmetric parabola opening upwards. 5. The graph covers $x$ values approximately from $-4$ to $4$ and $y$ values from $0$ to $16$. This is how you get the graph of $y = x^2$.