In the formula p(x) = -.1x^2 + 50x -300, could you describe the meaning of the number -.1 and -300 in the formula?
Certainly! In the given formula p(x) = -.1x^2 + 50x - 300, the numbers -.1 and -300 have specific meanings.
1. The number -.1: This number (-.1) is the coefficient of the x^2 term in the formula. The coefficient represents the rate of change or the slope of the quadratic function. In this case, since the coefficient is negative (-.1), it indicates that the quadratic function has a downward-opening shape. It means that as the value of x increases, the value of p(x) decreases.
2. The number -300: In the formula, -300 is the constant term or the y-intercept. It represents the value of p(x) when x is equal to zero. In this case, a value of -300 means that when x is zero, p(x) will have a value of -300.
To better understand the meaning of the numbers, you can also graph the quadratic function to visualize its shape and behavior. By plotting points on a graph, you can observe how the coefficient affects the shape of the graph and how the y-intercept determines where the graph intersects the y-axis.