Cubic (Leaving Cert Mathematics): Flashcards

3

$f(x)=ax^3+bx^2+cx+d$

$a \ne 0$

One or two

Three

Starts $-\infty$ (left), rises to $+\infty$ (right)

Starts $+\infty$ (left), falls to $-\infty$ (right)

Where graph crosses $x$-axis, $f(x)=0$

One real root (and two complex roots)

Three real roots

Sign and magnitude of $a$

$f(x)=0$