Last updated on Sep 20, 2026

Determining the Rule for the Graph of a Polynomial (VCE SSCE Mathematical Methods): Quizzes

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Determining the Rule for the Graph of a Polynomial

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10 questions from this quiz

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How many points are needed to determine a polynomial of degree $n$ ?

$n + 1$ points

How many points are needed to find the equation of a cubic function?

4 points

What form should you use if you can identify the point of inflection $(h, k)$ ?

$y = a(x - h)^3 + k$

If a graph crosses the x-axis at $x = 1, 2, 3$ , what form should you use?

$y = a(x - 1)(x - 2)(x - 3)$

If graph touches at $x = 2$ and crosses at $x = 5$ , what form applies?

$y = a(x - 2)^2(x - 5)$

What does it mean when a graph touches the x-axis at a point?

Repeated factor (squared)

For $y = a(x - 1)^3 + 3$ , point $(2, 11)$ is on graph. Find $a$ .

$a = 8$

When should you use the general form $y = ax^3 + bx^2 + cx + d$ ?

When no clear pattern is obvious

What does 'touch means twice' refer to?

Factor appears squared

What is often the easiest additional point to use when finding $a$ ?

The y-intercept ( $x = 0$ )

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