1. **State the problem:** Find the turning point of the curve given by the quadratic function $$y = 2x^2 - 20x + 58$$ by completing the square. 2. **Recall the formula and method:** A quadratic function in the form $$y = ax^2 + bx + c$$ can be rewritten by completing the square as $$y = a(x - h)^2 + k$$, where $$(h, k)$$ is the turning point. 3. **Start completing the square:** $$y = 2x^2 - 20x + 58$$ Factor out the coefficient of $x^2$ from the first two terms: $$y = 2(x^2 - 10x) + 58$$ 4. **Complete the square inside the parentheses:** Take half of the coefficient of $x$, which is $-10$, half is $-5$, then square it: $$(-5)^2 = 25$$. Add and subtract 25 inside the parentheses: $$y = 2(x^2 - 10x + 25 - 25) + 58$$ 5. **Rewrite as a perfect square and simplify:** $$y = 2((x - 5)^2 - 25) + 58$$ Distribute the 2: $$y = 2(x - 5)^2 - 50 + 58$$ Simplify constants: $$y = 2(x - 5)^2 + 8$$ 6. **Identify the turning point:** The function is now in vertex form $$y = a(x - h)^2 + k$$ with $$h = 5$$ and $$k = 8$$. **Therefore, the turning point is at** $$(5, 8)$$.