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.

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.

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
O wa lori Android, Windows, macOS, ati Linux

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

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
O wa lori Android, Windows, macOS, ati Linux

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
O wa lori Android, Windows, macOS, ati Linux

Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe

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.

Ṣe igbasilẹ ohun elo naa lori Google Playstore

Gbogbo ohun ti o nilo lati ṣe dara julọ ninu JAMB, WAEC ati NECO.

Green Bridge CBT Mobile App
Asiko ẹkọ AI ti ara ẹni Chat Assistant
Ẹgbẹẹgbẹrun Awọn Ibeere Atijọ JAMB, WAEC & NECO
Fiwọn 1200 Awọn akọsilẹ Ẹkọ ju.
Atilẹyin Aisinipo - Kọ ẹkọ Nigbakugba, Nibi gbogbo
Tẹ̀dí Green Bridge
Àkójọpọ̀ Ìtàn Lítíréṣọ̀ & Ìbéèrè Tó Lè Dáyéé ṣẹ́lẹ̀
Tẹle iṣẹ ṣiṣe rẹ ati ilọsiwaju rẹ.
Àlàyé tí ó jinlẹ̀ fún ìmòye tó jinlẹ̀.