Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem15

Levels 11&12 Video Solutions 2013 problem15

Video Transcription

Video Summary

The function \( w(x) = (a - x)(b - x)^2 \), with \( a < b \), has \( a \) and \( b \) as its x-intercepts. Near \( x = a \), \( w(x) \) behaves like a line and crosses the x-axis, while near \( x = b \), it behaves like a parabola, touching the x-axis. Thus, the graph first crosses and then touches the axis at intercepts. To select the correct graph, we analyzed end behavior: as \( x \to \infty \), \( w(x) \) decreases to \(-\infty\), which corresponds to graph choice \( a \).

Keywords

function behavior

x-intercepts

end behavior

graph analysis

parabola