How to Find the Slope of a Parabola

To find the slope of a parabola at a specific point, you need to use calculus, specifically the concept of derivatives. Here’s a step-by-step explanation:

1. Understand the Equation: A parabola is typically represented by a quadratic equation in the form y = ax² + bx + c, where a, b, and c are constants.
2. Find the Derivative: The derivative of the quadratic equation gives the slope of the tangent line at any point on the parabola. The derivative of y = ax² + bx + c is dy/dx = 2ax + b.
3. Plug in the x-coordinate: To find the slope at a specific point, substitute the x-coordinate of that point into the derivative. For example, if you want to find the slope at x = 2, you would calculate dy/dx = 2a(2) + b.
4. Calculate the Slope: Perform the calculation to find the slope. For instance, if a = 1 and b = 3, then dy/dx = 2(1)(2) + 3 = 7. So, the slope at x = 2 is 7.

This method allows you to find the slope of the parabola at any given point by using the derivative of its equation.