Last updated on Sep 22, 2026

Graph Parabolas (HSC SSCE Mathematics Advanced): Quizzes

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Graph Parabolas

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For $f(x) = ax^2 + bx + c$ , when does the parabola open upward?

When $a > 0$

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

The y-intercept

What is the formula for the axis of symmetry of a parabola?

$x = -\frac{b}{2a}$

If discriminant $\Delta = 0$ , how many x-intercepts does the parabola have?

Exactly one

What is the domain of any parabola $f(x) = ax^2 + bx + c$ ?

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

For concave up parabola with vertex y-coordinate $k = -3$ , what is the range?

$[-3, \infty)$

What does discriminant $\Delta < 0$ indicate about x-intercepts?

No x-intercepts

What is the x-coordinate of the vertex for $f(x) = ax^2 + bx + c$ ?

$-\frac{b}{2a}$

How does a larger value of $|a|$ affect the parabola's shape?

Makes it steeper (narrower)

To find the y-intercept, what value do you substitute for $x$ ?

$0$

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Graph Parabolas (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

For f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c, when does the parabola open upward?

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

What is the formula for the axis of symmetry of a parabola?

If discriminant Δ=0\Delta = 0Δ=0, how many x-intercepts does the parabola have?

What is the domain of any parabola f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c?

For concave up parabola with vertex y-coordinate k=−3k = -3k=−3, what is the range?

What does discriminant Δ<0\Delta < 0Δ<0 indicate about x-intercepts?

What is the x-coordinate of the vertex for f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c?

How does a larger value of ∣a∣|a|∣a∣ affect the parabola's shape?

To find the y-intercept, what value do you substitute for xxx?

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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

For $f(x) = ax^2 + bx + c$ , when does the parabola open upward?

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

If discriminant $\Delta = 0$ , how many x-intercepts does the parabola have?

What is the domain of any parabola $f(x) = ax^2 + bx + c$ ?

For concave up parabola with vertex y-coordinate $k = -3$ , what is the range?

What does discriminant $\Delta < 0$ indicate about x-intercepts?

What is the x-coordinate of the vertex for $f(x) = ax^2 + bx + c$ ?

How does a larger value of $|a|$ affect the parabola's shape?

To find the y-intercept, what value do you substitute for $x$ ?