A cubic equation is a polynomial equation of degree 3. Its general form is:
\[
ax^3 + bx^2 + cx + d = 0
\]
where \( a \neq 0 \). The graph of a cubic function can have one or two turning points and may intersect the x-axis up to three times.
Properties
Always has at least one real root.
Can have either one or three real roots.
Graph can have up to two turning points (local maxima and minima).
End behavior: As \( x \to \infty \), \( y \to \infty \) if \( a > 0 \); and \( y \to -\infty \) if \( a < 0 \).
