Last updated on Oct 24, 2026

Completing the Square (HSC SSCE Mathematics Advanced): Flashcards

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Completing the Square

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What completing the square transforms

Standard form to vertex form

Vertex form of a quadratic

$a(x - h)^2 + k$

Turning point from $a(x - h)^2 + k$

$(h, k)$

Axis of symmetry from $a(x - h)^2 + k$

$x = h$

Key step when $a = 1$ : do what with coefficient of $x$

Halve it, then square it

First step when $a \neq 1$

Factor out $a$ from first two terms

Value of $h$ in $(x + 3)^2$

$h = -3$

Opening direction when $a > 0$

Upward

What completing the square creates

Perfect square trinomial

Most common mistake in completing the square

Forgetting to subtract what you added

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Completing the Square (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

What completing the square transforms

Vertex form of a quadratic

Turning point from a(x−h)2+ka(x - h)^2 + ka(x−h)2+k

Axis of symmetry from a(x−h)2+ka(x - h)^2 + ka(x−h)2+k

Key step when a=1a = 1a=1: do what with coefficient of xxx

First step when a≠1a \neq 1a=1

Value of hhh in (x+3)2(x + 3)^2(x+3)2

Opening direction when a>0a > 0a>0

What completing the square creates

Most common mistake in completing the square

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Turning point from $a(x - h)^2 + k$

Axis of symmetry from $a(x - h)^2 + k$

Key step when $a = 1$ : do what with coefficient of $x$

First step when $a \neq 1$

Value of $h$ in $(x + 3)^2$

Opening direction when $a > 0$