1. **State the problem:** Graph the inequality $y > x^2 - 8x + 17$. 2. **Rewrite the quadratic in vertex form:** To find the vertex, complete the square for $x^2 - 8x + 17$. 3. Use the formula for completing the square: $$x^2 - 8x + 17 = (x^2 - 8x + 16) + 1 = (x - 4)^2 + 1$$ 4. **Interpret the vertex form:** The vertex is at $(4, 1)$, and the parabola opens upward because the coefficient of $x^2$ is positive. 5. **Graph the parabola:** Plot the vertex at $(4, 1)$ and sketch the parabola opening upward. 6. **Graph the inequality:** Since the inequality is $y > (x - 4)^2 + 1$, use a dashed line for the parabola to indicate points on the parabola are not included. 7. **Test a point to determine shading:** Choose a point not on the parabola, for example, $(4, 2)$. 8. Evaluate the parabola at $x=4$: $$y = (4 - 4)^2 + 1 = 0 + 1 = 1$$ 9. Since $2 > 1$ is true, the point $(4, 2)$ satisfies the inequality, so shade the region above the parabola. **Final answer:** The graph is the parabola $y = (x - 4)^2 + 1$ with a dashed line and shading above it.