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Completed Square Form (HSC SSCE Mathematics Advanced): Quizzes

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Completed Square Form

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What is the vertex of $f(x) = (x - 5)^2 + 3$ ?

$(5, 3)$

What is the axis of symmetry for $f(x) = 2(x + 4)^2 - 7$ ?

$x = -4$

If $a < 0$ in $f(x) = a(x - h)^2 + k$ , what is the concavity?

Concave down (opens downward)

What is the range of $f(x) = 3(x - 1)^2 + 2$ ?

$[2, \infty)$

What is the range of $f(x) = -(x + 2)^2 + 5$ ?

$(-\infty, 5]$

What is the domain of any quadratic function?

$\mathbb{R}$

How does larger | $a$ | affect the parabola in $f(x) = a(x - h)^2 + k$ ?

Makes it narrower

What is $x^2 - 4x + 1$ in completed square form?

$(x - 2)^2 - 3$

What must you do first for non-monic quadratics before completing the square?

Factorise $a$ from first two terms

In $f(x) = -2(x + 1)^2 + 6$ , what is the vertex?

$(-1, 6)$

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Completed Square Form (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What is the vertex of f(x)=(x−5)2+3f(x) = (x - 5)^2 + 3f(x)=(x−5)2+3?

What is the axis of symmetry for f(x)=2(x+4)2−7f(x) = 2(x + 4)^2 - 7f(x)=2(x+4)2−7?

If a<0a < 0a<0 in f(x)=a(x−h)2+kf(x) = a(x - h)^2 + kf(x)=a(x−h)2+k, what is the concavity?

What is the range of f(x)=3(x−1)2+2f(x) = 3(x - 1)^2 + 2f(x)=3(x−1)2+2?

What is the range of f(x)=−(x+2)2+5f(x) = -(x + 2)^2 + 5f(x)=−(x+2)2+5?

What is the domain of any quadratic function?

How does larger |aaa| affect the parabola in f(x)=a(x−h)2+kf(x) = a(x - h)^2 + kf(x)=a(x−h)2+k?

What is x2−4x+1x^2 - 4x + 1x2−4x+1 in completed square form?

What must you do first for non-monic quadratics before completing the square?

In f(x)=−2(x+1)2+6f(x) = -2(x + 1)^2 + 6f(x)=−2(x+1)2+6, what is the vertex?

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Solve Equations

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Introduction to Rates of Change

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Exponential Functions

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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 Flashcards 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

What is the vertex of $f(x) = (x - 5)^2 + 3$ ?

What is the axis of symmetry for $f(x) = 2(x + 4)^2 - 7$ ?

If $a < 0$ in $f(x) = a(x - h)^2 + k$ , what is the concavity?

What is the range of $f(x) = 3(x - 1)^2 + 2$ ?

What is the range of $f(x) = -(x + 2)^2 + 5$ ?

How does larger | $a$ | affect the parabola in $f(x) = a(x - h)^2 + k$ ?

What is $x^2 - 4x + 1$ in completed square form?

In $f(x) = -2(x + 1)^2 + 6$ , what is the vertex?