FUNGSI KUADRATIK (QUADRATIK FUNCTION) SIRI 2

Cantiknya kucing-kucing ni. Dok wat benda tu? Kalau tengok anak-anak kucing ni, rasa nyaman sikit kepala. Depa manja dan menghiburkan. Tetapi kalau tengok soalan Addmath, aduh sakitnya kepala. Berdenyut-denyut.

Dipendekkan cerita, sakit kepala ke, sakit mata ke, sakit kepala lulut ke, jom kita belajar Addmath.

Dalam siri (1) dahulu, MENGENAL FUNGSI KUADRATIK (QUADRATIC FUNCTION) SIRI 1, saya telah menerangkan cara bagaimana mencari titik bucu (vertec) bagi sesuatu graf. Anda patut belajar dengan lebih mahir cara tersebut, kerana ia menolong anda menjadi pakar Addmath suatu masa nanti.

Mari kita tengok soalan berikut. 

SOALAN PERTAMA
Find the vertex and intercepts of y = 3x² + x – 2 and graph; remember to label the vertex and the axis of symmetry.

How to get the y intercept? Take x = 0. Put x = 0 into the original equation. So you get y = 3 0)² + 0 - 2 = -2. Then the y-intercept is the point (0, –2). 

 How to find the x-intercept?, just set y equal to zero or y = 0, and solve:

0 = 3x² + x – 2

By using your calculator, you will get x = -1, 2/3

Then the x-intercepts are at the points (–1, 0) and ( ²/₃, 0).

How to find the axis-symentry?

Ada 2 cara (method) yang boleh digunakan.

[1] CARA MUDAH CIKGU  

Dalam persamaan kat atas, a = 3, b =1, c = -2 

so, x = - b/2a

x = - 1/2(3) = - 1/6

maka x = -1/6

[2] CARA BIASA DALAM KELAS  

The axis of symmetry is halfway between the two x-intercepts at (–1, 0) and at ( ²/₃ , 0); So by using this formula

x = (x1 + x2) / 2. 

we can get x =  (–1 + 2/3) / 2 = (–1/3) / 2 = –1/6

To find the vertec?    Sebelum ini awak dah dapat x =  -1/6. Masukan sahaja ke dalam persamaan asal.

y = 3x² + x – 2

y = 3(-1/6) ² + (-1/6)  – 2

y = -25/12 

Koordinat bucu (vertc) = (-1/6, -25/12).

What's your  listing answer?

The complete answer is a listing of the vertex, the axis of symmetry, and all three intercepts, along with a nice neat graph:

The vertex is at ( ^–1/₆ , ^–25/₁₂ ), the axis of symmetry is the line x = ^–1/₆ , and the intercepts are at (0, –2), (–1, 0), and ( ²/₃, 0).

Menggunakan semua maklumat di atas, sila bina graf yang sesuai dari persamaan di atas. Buat sendiri sampai jadi. He2.

MARI KITA TENGOK CONTOH KEDUA. Anda jangan panik dan takut. Tenang-tenang jew. Otak mesti kosong dari sebarang tanggapan negatif. Kalau dok kata payah, susah dan sebagainya, sampai bila pun anda tak dapat skor Addmath.  Sebelum kita melihat soalan kedua tu, elok kita tengok kucing seekor ni. Comelnya. .Dia sedang bercakap dengan 2 ekor anak itik.

SOALAN KEDUA
Find the intercepts, the axis of symmetry, and vertex of y = x² – x – 12.

To find the y-intercept,  set x equal to 0 (take x = 0) and solve:

Then you get y = -12

So, the point = (0, -12)

To find the x-intercept,  set y equal to 0 (take y = 0) and solve:

0 = x² – x – 12.

Use your calculator, so you get x = 4 and -3.

So, the point = (4, 0) and (-3, 0) 

To find the vertex, please look at the coefficients: a = 1 and b = –1. 

Plugging into the formula x = -b/2a, 

so you get x = - (-1) / (2X1) = -1/2

To find the value of y, just  plug or put  x =  1/2  into the equation  y = x² – x – 12, and simplify it. You will then get y = -12.25

So, the vertec (bucu) = ( 1/2, -12.25) 

To find the axis symentry, refer to x = 1/2 as you get before

so, the axis symentry, x = 1/2. 

Whats your lisitng answer?

The vertex is at the point (0.5, –12.25),

the axis of symmetry is the line x = 0.5,

and the intercepts are at the points (0, –12),  (–3, 0), and (4, 0).

Saya harap anda sudah faham sedikit sebanyak berkenaan tajuk ini. Jangan bazirkan apa yang saya berikan kepada anda di sini. Fahami dan gunakan apa yang anda dapat.

Sebagai pengesahan bahawa anda faham, tolong siapkan tutorial di bawah. Cari semua maklumat yang diperlukan seperti berikut : y-intercept, x-intercept, axis of symentry and the vertec.

[1].  y = 3x² +  x – 10.

[2].  y = 2x² – 9x + 12.

[3]   y = 3x² + x – 12.

Sekian. Terima kasih. 

DI RUMAH. 2.2.2013. 8.56 AM.