(10) \( -x^{2}+20 x-64 \)

Did you know that the quadratic equation \( -x^{2}+20x-64 \) represents a parabola that opens downwards? The vertex of this parabola can give you interesting information about its maximum value. By completing the square or using the vertex formula, we find the vertex at \( x = 10 \), making it the highest point on the curve! Now, here’s a fun way to connect this equation to real-world applications: think of it as modeling profit! If you imagine \( x \) as the number of items produced and sold, this equation might represent the profit generated from selling a certain quantity of goods. Finding the maximum profit is crucial for businesses, and using quadratic equations is a fantastic way to optimize operations!