A quadratic passes through (5,0), has symmetry axis x=2 and minimum −9. Find a,b,c.

01 / Standard#Your turn

f(x)=ax^2+bx+c

Official paper · jm01-2022 · II.1(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Start with vertex form.

Hint 2

Use the point (5,0) to find the scale.

Worked solution

a=1, b=−4, c=−5.

Checks and common pitfalls: The minimum specifies the vertex ordinate, not the constant term c.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write f(x)=a(x−2)²−9 with a>0.
$0=9a-9\implies a=1$
Expand the result.
$f(x)=(x-2)^2-9=x^2-4x-5$

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

2022 JM01