a. To graph the relation \ P = {1}/{5}x^2 + 4x + 60 \), we'll plot points for different values of \x\) and calculate the corresponding \P\) values using equation. Then, we'll plot these points on a graph. b. This relation is quadratic because it has a squared term (\(x^2 \) in the equation. Another way to see this is by noting that the graph of a quadratic equation is a parabola, and the given equation has the form of a quadratic function. the c. The direction of opening of the parabola is downward because the coefficient of the \(x^2 \) term (-{1}{5}) is negative. Since the coefficient of the \(x^2 \) term negative, the parabola opens downward, indicating that the profit function has a maximum. We know this because the coefficient of \(x^2 \) is negative. is d. To find the P \-intercept, we set \ x = 0 \) in the equation and solve for P \). \P = {1}{5}(0)^2 + 4(0) + 60 = 60 \) The P-intercept is \(0, 60) \). This represents the initial profit of the company in 2020 when \( x = 0 \). Yes, it makes sense that this is a new company because at the beginning (in 2020), the profit is $60 million. As the company grows and operates, the profit can increase or decrease based on various factors.