Kenneth ChengMathematical modeling
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Find the y-intercept P and vertex Q.

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TOPIC 01

2026 JM01

The vertex ordinate is 9, not the constant term 5.

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01 / Standard#Your turn

Find the y-intercept P and vertex Q.

y=−x2+4x+5y=-x^2+4x+5

Official paper · jm01-2026 · II.2(a) · PDF 4

Official original and suggested answers ↗ · Suggested answer PDF page 7

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Substitute x=0 for P.
Hint 2
Complete the square for Q.
Worked solution

  1. At x=0 the ordinate is 5.

    P=(0,5)P=(0,5)

  2. The square vanishes at the vertex.

    y=9−(x−2)2,Q=(2,9)y=9-(x-2)^2,\quad Q=(2,9)

P=(0,5), Q=(2,9).

Checks and common pitfalls: The vertex ordinate is 9, not the constant term 5.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • At x=0 the ordinate is 5.
    P=(0,5)P=(0,5)
  • The square vanishes at the vertex.
    y=9−(x−2)2,Q=(2,9)y=9-(x-2)^2,\quad Q=(2,9)

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