Graphs 6

3 marks · Normal

Write down the algebraic form of a cubic equation for a graph with a single turning point and which passes through the point (1, 0).

Give your answer in the form .

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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y = a(x-1)^3

Also accept: y = (x-1)^3; y = a(x-1)^3, a \neq 0

Common mistakes: Using (x+1) instead of (x-1); Using quadratic instead of cubic

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Marking points

M1 · 1 mark · Chooses a cubic form y = a(x-h)^3 for a single turning point.

M2 · 1 mark · Substitutes point (1,0) into the expression to find h=1.

A1 · 1 mark · Gives a correct algebraic formula: y = a(x-1)^3 (or y = (x-1)^3).

Worked solution

A cubic with a single turning point can be written as .

It passes through (1, 0):

So .

General answer: .