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Families of Cubic Polynomial Functions (VCE SSCE Mathematical Methods): Quizzes

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Families of Cubic Polynomial Functions

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What is a family of cubic functions?

A set sharing common form or property

What are parameters in cubic function families?

Values like $a$ , $b$ , $h$ , $k$ that vary

What does the form $y = ax^3$ where $a > 0$ represent?

Vertical dilations of $y = x^3$

Why does $y = ax^3 + bx^2 + cx$ pass through the origin?

It has no constant term

For $y = a(x - h)^3 + k$ , where is the point of inflection?

At $(h, k)$

Given $f(x) = a(x - h)^3 + k$ and pt of inflection, what else is needed to find $a$ ?

One additional point

If three x-axis intercepts are known, what else is needed to find $a$ in factored form?

One additional point

What does it mean when a cubic graph touches (not crosses) the x-axis at a point?

That factor is repeated

How many points are needed to find the general form $f(x) = ax^3 + bx^2 + cx + d$ ?

Four points

In factored form $y = a(x - 1)(x + 2)(x - 4)$ , what are the x-axis intercepts?

$1$ , $-2$ , and $4$

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Families of Cubic Polynomial Functions (VCE SSCE Mathematical Methods): Quizzes

Practise the questions

What is a family of cubic functions?

What are parameters in cubic function families?

What does the form y=ax3y = ax^3y=ax3 where a>0a > 0a>0 represent?

Why does y=ax3+bx2+cxy = ax^3 + bx^2 + cxy=ax3+bx2+cx pass through the origin?

For y=a(x−h)3+ky = a(x - h)^3 + ky=a(x−h)3+k, where is the point of inflection?

Given f(x)=a(x−h)3+kf(x) = a(x - h)^3 + kf(x)=a(x−h)3+k and pt of inflection, what else is needed to find aaa?

If three x-axis intercepts are known, what else is needed to find aaa in factored form?

What does it mean when a cubic graph touches (not crosses) the x-axis at a point?

How many points are needed to find the general form f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + df(x)=ax3+bx2+cx+d?

In factored form y=a(x−1)(x+2)(x−4)y = a(x - 1)(x + 2)(x - 4)y=a(x−1)(x+2)(x−4), what are the x-axis intercepts?

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

What does the form $y = ax^3$ where $a > 0$ represent?

Why does $y = ax^3 + bx^2 + cx$ pass through the origin?

For $y = a(x - h)^3 + k$ , where is the point of inflection?

Given $f(x) = a(x - h)^3 + k$ and pt of inflection, what else is needed to find $a$ ?

If three x-axis intercepts are known, what else is needed to find $a$ in factored form?

How many points are needed to find the general form $f(x) = ax^3 + bx^2 + cx + d$ ?

In factored form $y = a(x - 1)(x + 2)(x - 4)$ , what are the x-axis intercepts?