a To graph the relation P 1 5 x 2 4x 60 we ll plot...

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Calculus

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

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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