Polynomial (Cubic & Quartic) Functions (Year 11)
Free printable Year 11 Mathematical Methods worksheet on cubic and quartic functions: factorising to find roots, expanding, evaluating and graphing (ACMMM017-019).
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Year 11 · Math worksheet
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Math
Functions: Polynomial (Cubic & Quartic) Functions
Expand, factorise, solve and evaluate cubic and quartic functions, and describe their end behaviour and graphs. (ACARA Mathematical Methods Unit 1: ACMMM017-019.)
- 1.Expand f(x) = (x + 2)(x - 2)(x - 3) into the form ax3 + bx2 + cx + d.
- 2.Expand f(x) = (x + 3)(x + 1)(x - 2) into the form ax3 + bx2 + cx + d.
- 3.Expand f(x) = (x + 2)(x - 1)(x - 2) into the form ax3 + bx2 + cx + d.
- 4.Solve f(x) = - 4x^2 + x + 6 = 0 by factorising to find all real roots.
- 5.Solve f(x) = - 4x^2 + x + 6 = 0 by factorising to find all real roots.
- 6.Solve f(x) = - 4x^2 + x + 6 = 0 by factorising to find all real roots.
- 7.For f(x) = - 2x^2 - x + 2, evaluate f(2).
- 8.For f(x) = + 2x^2 - 9x - 18, evaluate f(-1).
- 9.A polynomial has leading term . Describe its end behaviour: what happens to f(x) as x -> +infinity and as x -> -infinity?
- 10.A polynomial has leading term -. Describe its end behaviour: what happens to f(x) as x -> +infinity and as x -> -infinity?
- 11.Solve the quartic f(x) = (x + 3)(x + 1)(x - 1)(x - 3) = 0. State all four roots and the end behaviour.
- 12.Sketch y = - 2x^2 - 5x + 6. The graph below plots the curve; confirm it cuts the x-axis at each root and identify the y-intercept.
Cubic through its three real roots.
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