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