Mathematics - Additional - 0606 CIE

Completing The Square And The Vertex

Bayani Gaba-gaba

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.

Manufura

  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.

Takardar Darasi

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

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Nazarin Darasi

Barka da kammala darasi akan Completing The Square And The Vertex. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

  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

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Yi Aikin Tambayoyin Gwaji

Kana son yin aikin tambayoyin gwaji kan Completing The Square And The Vertex? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.

Sauke Manhajar Daga Google Playstore

Duk abin da kake buƙata don yin fice a JAMB, WAEC & NECO.

Green Bridge CBT Mobile App
Keɓantaccen Mataimaki na Tattaunawa na Koyo na AI
Dubban Tambayoyi na JAMB, WAEC & NECO na Baya.
Fiye da Lura-Luran Darussa 1200
Tallafin Wajen Layi - Koyo Kowane Lokaci, Ko'ina
Jadawalin Gadar Kore.
Takaitaccen Bayanin Adabi & Tambayoyin Da Za Su Iya Tashi
Bibiye Ayyukanka da Ci Gaban Ka
Cikakken Bayani don Koyon Fahimta.