Practice Standard, Factored, And Vertex Forms (3) - Cubic Functions - IB 10 Mathematics

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Write the cubic function in standard form: f(x) = (x - 1)(x + 2)(x - 3).
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Expand the factors step-by-step.
Question 2.
Identify the roots of: f(x) = 3(x - 2)(x + 1)(x + 4).
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Set each factor equal to zero.
3Question 3.
What is the standard form of a cubic function?
- f(x) = ax³ + bx² + cx + d
- f(x) = a(x - r₁)(x - r₂)(x - r₃)
- f(x) = a(x - h)³ + k
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Remember the general polynomial form.
4Question 4.
True or False: The factored form of a cubic function makes it easier to find its roots.
- True
- False
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Think about how roots are identified in each form.
Question 5.
A cubic function has roots at x = -2, x = 1, and x = 3. Write its factored form and find the standard form.
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Expand every factor systematically.
Question 6.
Given f(x) = 2x³ + 3x² - 8x - 12, determine its turning points without solving for roots, then sketch the graph.
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Numerically analyze coefficients before graphing.

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