Equations of Tangents and Normals

The video tutorial covers finding gradients by differentiating functions, specifically focusing on y = x^2 and y = 4x^3 + 2x^2 - 3x + 2. It explains how to find equations of tangents and normals, solve quadratic equations, and determine where these lines intersect the axes. The tutorial also discusses finding tangents parallel to a given line and emphasizes the relationship between gradients of perpendicular lines.

Explain how to solve the quadratic equation derived from the tangent's gradient.

How do you find the points where the tangent crosses the x-axis and y-axis?

What are the coordinates of the points A, B, C, and D found in the tangent and normal equations?