Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

The algebra lesson involves finding the sum of the x-coordinates where 2012 lines, each parallel to \( y = x \), intersect the parabola \( y = x^2 \). Each line can be represented as \( y = x + k \), intersecting the parabola at two points. Solving for the intersection gives the quadratic equation \( x^2 - x - k = 0 \), where the sum of the roots (x-coordinates) is 1, according to Vieta's formulas. With 2012 lines, each contributing a sum of 1, the total sum of all x-coordinates is 2012.

Keywords

algebra

parabola

intersection

x-coordinates

Vieta's formulas