Translate that graph 3 units left, then 3 units up. Find its new function.

01 / Standard#Your turn

f(x)=(x-2)^2-9

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A left shift replaces x by x+3.

Hint 2

An upward shift adds 3 outside the function.

Worked solution

y=(x+1)²−6.

Checks and common pitfalls: Horizontal and vertical changes act in different places in the formula.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Apply the two transformations.
$y=f(x+3)+3$
Simplify.
$y=(x+1)^2-6=x^2+2x-5$

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

2022 JM01