Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem18

11&12 Video Solutions 2011 problem18

Video Transcription

Video Summary

The video transcript discusses determining which inequality is not necessarily true for a given point on a parabola. It states that the parabola is concave up, leading to a positive leading coefficient. From substituting \( x = 1 \), the equation yields \( A + B + C = -10 \), confirming it's negative. For a concave-up parabola, the vertex is to the right of point A, leading to \( -b > 2a \), implying \( b \) is negative. The quadratic's discriminant, \( b^2 - 4ac > 0 \), confirms 2 x-intercepts. Thus, options A, B, C, and D are validated, leaving option E as potentially false.

Keywords

parabola

inequality

concave up

discriminant

vertex