Read off the slope of parabolas

Determine the slope of parabolas

The slope of Parabolas can be determined particularly easily with the derivation function. This is because the slope of a parabola at a certain point on the curve is just as great as the slope of the tangent to the parabola which runs through this point.

• Have a parabola with the functional equation f (x) = ax²+ bx + c and the point P (x₁| y₁), then m applies to the slope of the tangent to the parabola at this point_t = f '(x₁).
• For example, if f is given by f (x) = 2x²+ 4x-2 and P (1 | 4), then f '(x) = 4x + 4 and f' (1) = 8. The slope m of the parabola at point P (1 | 4) is 8.
• Incidentally, the slope is different at each point of the parabola. So at point Q (2 | 14) it is m = f '(2) = 12.
• But can you also read this value from the coordinate system? Unfortunately, you cannot read off the slope directly, you can only estimate it. With a little practice, you can estimate the gradient relatively well after just a few attempts. You will only see how far you are off when you calculate the slope exactly with the help of the derivative.
  instagram viewer


Explain the differential function clearly to the math tutor

The differential function is one of the first steps in analysis and will ...

Read off certain gradients

• At one point, however, you can easily read the slope. Because of f '(x_s) = 0 the slope of the parabola 0. You can therefore easily read this value from the drawing.
• But for all other points, too, you will be able to calculate the gradient faster and faster as you gain experience. At some point you will be able to specify the derivative of a quadratic function very quickly and then it is only a stone's throw to the size you are looking for.

As you can see, it is not particularly difficult to specify the slope of a parabola at different points on the curve. All you need is the function equation and the derivative.