Algebra 3 summary

Key learning points

• Complete the square for vertex form.
• Cancel factors only — never bare terms across a sum.
• Change the subject with inverse operations in reverse order.
• State excluded values after cancelling.

Worked example 1 — Complete square

Write $x^2+6x+5$ in completed-square form.

Working

Half of 6 is 3; adjust the constant.

Worked example 2 — Complete the square for vertex form

Use this method from the Algebra 3 sheet: Complete the square for vertex form.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Cancel factors only — never bare terms across a sum

Use this method from the Algebra 3 sheet: Cancel factors only — never bare terms across a sum.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Change the subject with inverse operations in reverse

Use this method from the Algebra 3 sheet: Change the subject with inverse operations in reverse order.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — State excluded values after cancelling

Use this method from the Algebra 3 sheet: State excluded values after cancelling.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.