1. **Stating the problem:** We need to draw the parabola given by the equation $$y + 5 = x(6 - x)$$ after rewriting it in standard form. 2. **Rewrite the equation:** Start with the given equation: $$y + 5 = x(6 - x)$$ Expand the right side: $$y + 5 = 6x - x^2$$ 3. **Isolate y:** Subtract 5 from both sides: $$y = 6x - x^2 - 5$$ 4. **Rewrite in standard quadratic form:** Rearranged as: $$y = -x^2 + 6x - 5$$ 5. **Identify the parabola characteristics:** - The coefficient of $$x^2$$ is $$-1$$, which means the parabola opens downward. - The vertex form can be found by completing the square. 6. **Complete the square:** $$y = -\left(x^2 - 6x\right) - 5$$ To complete the square inside the parentheses: $$x^2 - 6x = (x^2 - 6x + 9) - 9 = (x - 3)^2 - 9$$ 7. **Substitute back:** $$y = -\left((x - 3)^2 - 9\right) - 5 = - (x - 3)^2 + 9 - 5 = - (x - 3)^2 + 4$$ 8. **Interpretation:** The vertex is at $$ (3, 4) $$. The parabola opens downward because of the negative coefficient. 9. **Summary:** The parabola equation in vertex form is: $$y = - (x - 3)^2 + 4$$ This form is useful for graphing the parabola. **Final answer:** $$y = -x^2 + 6x - 5$$ or equivalently $$y = - (x - 3)^2 + 4$$