Mathematics - Additional - 0606 CIE

Graphs Of Cubic Polynomials

Akopọ

A cubic given as a product of three linear factors is easy to sketch: its roots are read straight from the factors, and its shape follows a predictable pattern. From the sketch you can solve equations and inequalities at a glance.

In this lesson you will sketch the graphs of cubic polynomials and their moduli when given as a product of three linear factors, labelling the intersections with the axes.

Awọn Afojusun

  1. Sketch the graphs of cubic polynomials and their moduli when given as a product of three linear factors, clearly labelling the intersections with the coordinate axes.

Ẹ̀kọ́ Ohùn

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Akọ̀wé Ẹ̀kọ́

Sketching a cubic from its factors is the fastest route to its roots, shape and behaviour, and it underpins solving cubic equations and inequalities.

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Ìdánwò Ẹ̀kọ́

Oriire fun ipari ẹkọ lori Graphs Of Cubic Polynomials. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.

Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.

Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.

  1. The roots of y = (x + 2)(x - 1)(x - 3) are: A. 2, 1, 3 B. -2, 1, 3 C. -2, -1, -3 D. 2, -1, 3 Answer: B
  2. The y-intercept of y = (x + 2)(x - 1)(x - 3) is: A. 0 B. 6 C. -6 D. 2 Answer: B
  3. A factor (x - 3) gives a root at: A. -3 B. 0 C. 3 D. 1/3 Answer: C
  4. To find the y-intercept of a curve you set: A. y = 0 B. x = 0 C. x = y D. x = 1 Answer: B
  5. For a positive leading coefficient, a cubic graph: A. falls to the right B. rises to the right C. is symmetric D. is a parabola Answer: B

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Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Graphs Of Cubic Polynomials? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.

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