Find the parameter range making the function strictly decreasing on (−1,∞).

01 / Standard#Your turn

f(x)=-3x^2+2(a-1)x+2

Official paper · jm01-2026 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the condition on pairs of points into strict decrease.

Hint 2

The vertex of this downward parabola must be at or left of −1.

Worked solution

Write the vertex coordinate.
$x_v=\frac{a-1}3$
To be decreasing throughout the open interval, the vertex may equal its left endpoint.
$\frac{a-1}3\le-1\iff a\le-2$

B: a≤−2.

Checks and common pitfalls: Equality is allowed: the interval excludes −1.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write the vertex coordinate.
$x_v=\frac{a-1}3$
To be decreasing throughout the open interval, the vertex may equal its left endpoint.
$\frac{a-1}3\le-1\iff a\le-2$

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

2026 JM01