Sketch the cubic on −3≤x≤1.2.

01 / Standard#Your turn

f(x)=x^3+3x^2-4

Official paper · jm02-2025 · 2(a)(v) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the repeated zero and the simple zero.

Hint 2

Include both endpoint values and the critical points.

Worked solution

Mark the interval endpoints and zeros.
$f(-3)=-4,\quad f(1.2)=2.048,\quad f(-2)=f(1)=0$
Join smoothly, increasing to (−2,0), decreasing to (0,−4), then increasing; change concavity at (−1,−2).

The plotted cubic touches the axis at −2 and crosses at 1.

Checks and common pitfalls: A double root touches rather than crosses the axis here.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Mark the interval endpoints and zeros.
$f(-3)=-4,\quad f(1.2)=2.048,\quad f(-2)=f(1)=0$
Join smoothly, increasing to (−2,0), decreasing to (0,−4), then increasing; change concavity at (−1,−2).

Think first. Reveal a hint when the class is ready.

2025 JM02