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Equations of Parabolas (HSC SSCE Mathematics Advanced): Quizzes

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Equations of Parabolas

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In standard form $f(x) = ax^2 + bx + c$ , what does the constant $c$ represent?

The y-intercept

In vertex form $f(x) = a(x - h)^2 + k$ , what point does $(h, k)$ represent?

The vertex

What does factorised form $f(x) = a(x - x_1)(x - x_2)$ reveal about a parabola?

The x-intercepts at $x_1$ and $x_2$

If the leading coefficient $a > 0$ , how does the parabola open?

Upward (concave up)

If $a < 0$ in a quadratic function, what is the concavity?

Concave down

Which form should you use when you know the vertex and one other point?

Vertex form

What is the domain of any parabola?

All real numbers $\mathbb{R}$

For a parabola with $a > 0$ and vertex $(2, -5)$ , what is the range?

$[-5, \infty)$

For a parabola with vertex $(3, 7)$ , what is the axis of symmetry?

$x = 3$

When two quadratics are equal for all $x$ , what must be true about their coefficients?

Corresponding coefficients are equal

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Equations of Parabolas (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

In standard form f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c, what does the constant ccc represent?

In vertex form f(x)=a(x−h)2+kf(x) = a(x - h)^2 + kf(x)=a(x−h)2+k, what point does (h,k)(h, k)(h,k) represent?

What does factorised form f(x)=a(x−x1)(x−x2)f(x) = a(x - x_1)(x - x_2)f(x)=a(x−x1​)(x−x2​) reveal about a parabola?

If the leading coefficient a>0a > 0a>0, how does the parabola open?

If a<0a < 0a<0 in a quadratic function, what is the concavity?

Which form should you use when you know the vertex and one other point?

What is the domain of any parabola?

For a parabola with a>0a > 0a>0 and vertex (2,−5)(2, -5)(2,−5), what is the range?

For a parabola with vertex (3,7)(3, 7)(3,7), what is the axis of symmetry?

When two quadratics are equal for all xxx, what must be true about their coefficients?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

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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 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 standard form $f(x) = ax^2 + bx + c$ , what does the constant $c$ represent?

In vertex form $f(x) = a(x - h)^2 + k$ , what point does $(h, k)$ represent?

What does factorised form $f(x) = a(x - x_1)(x - x_2)$ reveal about a parabola?

If the leading coefficient $a > 0$ , how does the parabola open?

If $a < 0$ in a quadratic function, what is the concavity?

For a parabola with $a > 0$ and vertex $(2, -5)$ , what is the range?

For a parabola with vertex $(3, 7)$ , what is the axis of symmetry?

When two quadratics are equal for all $x$ , what must be true about their coefficients?