1. **State the problem:** We need to graph the function $f(x) = x^2 - 2x + 7$ and plot its vertex and another point on the parabola. 2. **Formula and rules:** The function is a quadratic in standard form $f(x) = ax^2 + bx + c$ where $a=1$, $b=-2$, and $c=7$. 3. **Find the vertex:** The vertex of a parabola $y = ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. Calculate: $$x = -\frac{-2}{2 \times 1} = \frac{2}{2} = 1$$ Find $f(1)$: $$f(1) = 1^2 - 2 \times 1 + 7 = 1 - 2 + 7 = 6$$ So the vertex is at $(1, 6)$. 4. **Plot another point:** Choose $x=0$ for simplicity. Calculate $f(0)$: $$f(0) = 0^2 - 2 \times 0 + 7 = 7$$ So another point is $(0, 7)$. 5. **Summary:** The parabola opens upwards (since $a=1 > 0$), vertex at $(1,6)$, and passes through $(0,7)$. This information can be used to sketch the graph on the coordinate grid with $x$-axis and $f(x)$-axis ranging from -10 to 10.