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Math Visualization 2

Visually Explore the shape of a parabola given in standard form. Understand the tangent and slope of the parabola

Slope of a Parabola by Tangent Line

The Standard form of a parabola is given by \(ax^2+bx+c \). Visually Explore the shape of the parabola for various values of it's coefficients \(a \), \(b \). and \(c \). What are its extends?

How to find the slope of such a parabola? Does the slope of a parabola a constant or it varies? For this a tangent line is drawn at a point \(A \) on the parabola. Slope of this tangent line is the slope of the parabola. Explore and understand what is a tangent line and how to obtain its equation. Can this be generalized to any curve? Compare with the previous article math visualization 1 and identify the difference.