Mathematics - Additional - 0606 CIE

Completing The Square And The Vertex

Muhtasari

Completing the square rewrites a quadratic so that its turning point is visible at a glance. From the rewritten form you can read off the maximum or minimum value and the line of symmetry without any further work.

In this lesson you will find the maximum or minimum value of a quadratic by completing the square, and use it to sketch the graph or find the range for a given domain.

Malengo

  1. Find the maximum or minimum value of a quadratic function by completing the square or by differentiation.
  2. Use the maximum or minimum value to sketch the graph of the function or to determine its range for a given domain.

Maelezo ya Somo

The completed-square form instantly gives the vertex and range of a quadratic, which is central to graph sketching and optimisation.

Inapatikana kwenye programu ya Green Bridge

Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Completing The Square And The Vertex. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.

Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.

  1. Complete the square: x^2 - 4x + 1 = A. (x - 2)^2 - 3 B. (x - 2)^2 + 1 C. (x - 4)^2 - 3 D. (x + 2)^2 - 3 Answer: A
  2. The vertex of y = (x - 2)^2 - 3 is: A. (2, 3) B. (2, -3) C. (-2, -3) D. (-2, 3) Answer: B
  3. For y = (x - 2)^2 - 3, the minimum value is: A. 2 B. -2 C. -3 D. 3 Answer: C
  4. In a(x - h)^2 + k, the vertex is a maximum when: A. a > 0 B. a < 0 C. a = 0 D. k > 0 Answer: B
  5. The line of symmetry of y = (x - 2)^2 - 3 is: A. x = -2 B. x = 2 C. y = -3 D. x = 3 Answer: B

Inapatikana kwenye programu ya Green Bridge

Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.

Maelezo kamili ya masomo yenye michoro
Msaidizi wa kujifunza wa AI
Soma bila mtandao, wakati wowote, mahali popote
Inapatikana kwa Android, Windows, macOS, na Linux

Inapatikana kwenye programu ya Green Bridge

Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.

Maelezo kamili ya masomo yenye michoro
Msaidizi wa kujifunza wa AI
Soma bila mtandao, wakati wowote, mahali popote
Inapatikana kwa Android, Windows, macOS, na Linux

Fanya Mazoezi ya Maswali ya Majaribio

Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Completing The Square And The Vertex? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.

Pakua Programu Kwenye Google Playstore

Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.

Green Bridge CBT Mobile App
Msaidizi wa Gumzo wa Kujifunza wa AI Uliobinafsishwa
Maelfu ya Maswali ya Zamani ya JAMB, WAEC & NECO
Zaidi ya Madaftari ya Masomo 1200
Msaada Nje ya Mtandao - Jifunze Wakati Wowote, Popote Pale
Ratiba ya Daraja la Kijani
Muhtasari wa Fasihi na Maswali Yanayoweza Kutokea
Fuata Utendaji na Maendeleo Yako
Maelezo ya Kina kwa Kujifunza kwa Kina