To solve the quadratic equation and inequality provided in the question: Given function: P(r) = -9r^2 + 8r + 1 A. To solve the quadratic equation -9r^2 + 8r + 1 = 0: -9r^2 + 8r + 1 = 0 This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula: r = (-b ± √(b^2 - 4ac)) / 2a In this case: a = -9, b = 8, c = 1 Substitute the values into the formula to find the solutions for r. B. To solve the quadratic inequality -9r^2 + 8r + 1 > 0: -9r^2 + 8r + 1 > 0 This inequality represents the regions where the monthly profit P(r) is greater than zero. We can find the intervals where the profit is positive by analyzing the sign of the quadratic expression. We can solve the inequality by finding the critical points and testing the intervals to determine when the inequality holds true. After solving both the equation and the inequality, we can interpret the solutions in the context of the relationship between monthly rent charged for space (r) and monthly profit (P(r)).