Last updated on Sep 20, 2026

Completed Square Form (HSC SSCE Mathematics Advanced): Flashcards

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Completed Square Form

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Other name for completed square form

Vertex form

General form of completed square

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

$(h, k)$ in $f(x) = a(x - h)^2 + k$

Vertex of the parabola

What parameter $a$ determines

Concavity and stretch

Concavity when $a > 0$

Concave up (opens upward)

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

$x = h$

Domain of quadratic function

All real numbers ( $\mathbb{R}$ )

Range when $a > 0$ (concave up)

$[k, \infty)$

Range when $a < 0$ (concave down)

$(-\infty, k]$

Key step for non-monic quadratics before completing square

Factorise $a$ from first two terms

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Completed Square Form (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Other name for completed square form

General form of completed square

(h,k)(h, k)(h,k) in f(x)=a(x−h)2+kf(x) = a(x - h)^2 + kf(x)=a(x−h)2+k

What parameter aaa determines

Concavity when a>0a > 0a>0

Axis of symmetry from f(x)=a(x−h)2+kf(x) = a(x - h)^2 + kf(x)=a(x−h)2+k

Domain of quadratic function

Range when a>0a > 0a>0 (concave up)

Range when a<0a < 0a<0 (concave down)

Key step for non-monic quadratics before completing 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

$(h, k)$ in $f(x) = a(x - h)^2 + k$

What parameter $a$ determines

Concavity when $a > 0$

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

Range when $a > 0$ (concave up)

Range when $a < 0$ (concave down)