Kenneth ChengMathematical modeling
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A parabola passes through (−2,0), (6,0), and (0,4). Find its maximum ordinate.

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TOPIC 01

2024 JM01

The negative leading coefficient makes the vertex a maximum.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

A parabola passes through (−2,0), (6,0), and (0,4). Find its maximum ordinate.

Official paper · jm01-2024 · I.11 · PDF 3

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A83\frac83
  2. Option B163\frac{16}3
  3. Option C44
  4. Option D88
  5. Option E1616

Working and explanation

BUILD THE REASONING

Hint 1
Use its two zeros to factor its equation.
Hint 2
The vertex is midway between the zeros.
Worked solution

  1. Determine the leading coefficient.

    y=a(x+2)(x−6),4=−12a  ⟹  a=−1/3y=a(x+2)(x-6),\quad4=-12a\implies a=-1/3

  2. Evaluate at the symmetry axis.

    x=2,y=−13(4)(−4)=163x=2,\quad y=-\frac13(4)(-4)=\frac{16}3

B: 16/3.

Checks and common pitfalls: The negative leading coefficient makes the vertex a maximum.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Determine the leading coefficient.
    y=a(x+2)(x−6),4=−12a  ⟹  a=−1/3y=a(x+2)(x-6),\quad4=-12a\implies a=-1/3
  • Evaluate at the symmetry axis.
    x=2,y=−13(4)(−4)=163x=2,\quad y=-\frac13(4)(-4)=\frac{16}3

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