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Graphs of Factorised Cubic Functions (VCE SSCE Mathematical Methods): Quizzes

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Graphs of Factorised Cubic Functions

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What is the general polynomial form of a cubic function?

$y = ax^3 + bx^2 + cx + d$ where $a \neq 0$

How many x-axis intercepts can a cubic function have?

One, two, or three

For $y = ax^3 + bx^2 + cx + d$ , what is the y-axis intercept?

$(0, d)$

For $y = (x - 1)(x + 2)(x + 1)$ , what are the x-axis intercepts?

$x = 1$ , $x = -2$ , $x = -1$

What effect does a negative coefficient of $x^3$ have on the graph?

Reflection in the x-axis

For a repeated factor $(x - a)^2$ , what happens to the sign of $y$ across $x = a$ ?

Same sign on both sides

How many x-axis intercepts does $y = (x - 1)^2(x + 3)$ have?

Two

What does a sign diagram show?

When an expression is positive or negative

If the coefficient of $x^3$ is positive, what happens as $x$ increases to the right?

Graph rises to the right

For $x^2 + 4x + 5$ , what does $\Delta = -4$ indicate about further factorization?

No further linear factors exist

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Graphs of Factorised Cubic Functions (VCE SSCE Mathematical Methods): Quizzes

Practise the questions

What is the general polynomial form of a cubic function?

How many x-axis intercepts can a cubic function have?

For y=ax3+bx2+cx+dy = ax^3 + bx^2 + cx + dy=ax3+bx2+cx+d, what is the y-axis intercept?

For y=(x−1)(x+2)(x+1)y = (x - 1)(x + 2)(x + 1)y=(x−1)(x+2)(x+1), what are the x-axis intercepts?

What effect does a negative coefficient of x3x^3x3 have on the graph?

For a repeated factor (x−a)2(x - a)^2(x−a)2, what happens to the sign of yyy across x=ax = ax=a?

How many x-axis intercepts does y=(x−1)2(x+3)y = (x - 1)^2(x + 3)y=(x−1)2(x+3) have?

What does a sign diagram show?

If the coefficient of x3x^3x3 is positive, what happens as xxx increases to the right?

For x2+4x+5x^2 + 4x + 5x2+4x+5, what does Δ=−4\Delta = -4Δ=−4 indicate about further factorization?

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

For $y = ax^3 + bx^2 + cx + d$ , what is the y-axis intercept?

For $y = (x - 1)(x + 2)(x + 1)$ , what are the x-axis intercepts?

What effect does a negative coefficient of $x^3$ have on the graph?

For a repeated factor $(x - a)^2$ , what happens to the sign of $y$ across $x = a$ ?

How many x-axis intercepts does $y = (x - 1)^2(x + 3)$ have?

If the coefficient of $x^3$ is positive, what happens as $x$ increases to the right?

For $x^2 + 4x + 5$ , what does $\Delta = -4$ indicate about further factorization?