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Completing the Square (HSC SSCE Mathematics Advanced): Quizzes

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Completing the Square

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What does completing the square transform a quadratic expression into?

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

In vertex form $a(x - h)^2 + k$ , what are the coordinates of the turning point?

$(h, k)$

If a quadratic is written as $(x + 3)^2$ , what is the value of $h$ ?

$h = -3$

When $a = 1$ , what is the key calculation needed to complete the square?

Halve coefficient of $x$ , then square

From vertex form $a(x - h)^2 + k$ , what is the axis of symmetry?

$x = h$

If $a > 0$ in vertex form $a(x - h)^2 + k$ , which way does the parabola open?

Upward

What is the most common error when completing the square if $a \neq 1$ ?

Not factoring out $a$ from first 2 terms

Complete the square for $x^2 + 6x + 5$ . What is the result?

$(x + 3)^2 - 4$

If $x^2 - 4x + 1 = (x - 2)^2 - 3$ , what is the turning point?

$(2, -3)$

For $x^2 + 8x$ , what value must be added and subtracted to complete the square?

$16$

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Completing the Square (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What does completing the square transform a quadratic expression into?

In vertex form a(x−h)2+ka(x - h)^2 + ka(x−h)2+k, what are the coordinates of the turning point?

If a quadratic is written as (x+3)2(x + 3)^2(x+3)2, what is the value of hhh?

When a=1a = 1a=1, what is the key calculation needed to complete the square?

From vertex form a(x−h)2+ka(x - h)^2 + ka(x−h)2+k, what is the axis of symmetry?

If a>0a > 0a>0 in vertex form a(x−h)2+ka(x - h)^2 + ka(x−h)2+k, which way does the parabola open?

What is the most common error when completing the square if a≠1a \neq 1a=1?

Complete the square for x2+6x+5x^2 + 6x + 5x2+6x+5. What is the result?

If x2−4x+1=(x−2)2−3x^2 - 4x + 1 = (x - 2)^2 - 3x2−4x+1=(x−2)2−3, what is the turning point?

For x2+8xx^2 + 8xx2+8x, what value must be added and subtracted to complete the square?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

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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

In vertex form $a(x - h)^2 + k$ , what are the coordinates of the turning point?

If a quadratic is written as $(x + 3)^2$ , what is the value of $h$ ?

When $a = 1$ , what is the key calculation needed to complete the square?

From vertex form $a(x - h)^2 + k$ , what is the axis of symmetry?

If $a > 0$ in vertex form $a(x - h)^2 + k$ , which way does the parabola open?

What is the most common error when completing the square if $a \neq 1$ ?

Complete the square for $x^2 + 6x + 5$ . What is the result?

If $x^2 - 4x + 1 = (x - 2)^2 - 3$ , what is the turning point?

For $x^2 + 8x$ , what value must be added and subtracted to complete the square?