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FUNGSIOLEHNOVIARTINIM: 11308502130081PRODI/KELAS: Matematika/4DMAKUL: Bahasa Inggris untuk ScienceDOSEN PENGAMPU: Ummi Afni M,SSFungsi : suatu bentuk hubungan matematis yang menyatakan hubungan ketergantungan (hub. fungsional) antara suatu variabel dengan variabel lain.

y = a + bx

Jenis-jenis fungsiFungsiF.PangkatF. PolinomF. LinierF. KuadratF. KubikF. Bikuadrat

Fungsi rasionalFungsi irrasionalFungsi non-aljabar (transenden)Fungsi aljabarF. EksponensialF. LogaritmikF. TrigonometrikF. Hiperbolik

31.Bentuk umum fungsi kuadrat y = f(x) ax2+bx+c dengan a,b, c R dan a 0 Grafik fungsi kuadrat berbentuk parabola simetris 2. Sifat-sifat Grafik Fungsi Kuadrat Berdasarkan nilai a (i) Jika a > 0 (positif), maka grafik terbuka ke atas. Fungsi kuadrat memiliki nilai ekstrim minimum, dinotasikan ymin atau titik balik minimum. (ii) Jika a < 0 (negatif), maka grafik terbuka ke bawah. Fungsi kuadrat memiliki nilai ekstrim maksimum, dinotasikan ymaks atau titik balik maksimum.

Berdasarkan Nilai Diskriminan (D) Nilai diskriminan suatu persamaan kuadrat adalah D = b2 4ac Hubungan antara D dengan titik potong grafik dengan sumbu X Jika D > 0 maka grafik memotong sumbu X di dua titik yang berbeda.Jika D = 0 maka grafik menyinggung sumbu X di sebuah titik.Jika D < 0 maka grafik tidak memotong dan tidak menyinggung sumbu X.

FUNGSI KUADRATKedudukan Grafik Fungsi Kuadrat Terhadap Sumbu X X(i)X(ii)X(iii)a > 0D > 0a > 0D = 0a > 0D < 0X(iv)X(v)a < 0D > 0a < 0D = 0X(vi)a < 0D < 0 FUNGSI KUADRAT3. Menggambar Grafik Fungsi Kuadrat Langkah-langkah menggambar grafik fungsi kuadrat : (i) Menentukan titik potong dengan sumbu X (y = 0) (ii) Menentukan titik potong dengan sumbu Y (x = 0) (iii) Menentukan sumbu simentri dan koordinat titik balik

Persamaan sumbu simetri adalah x =

Koordinat titik puncak / titik balik adalah

(iv) Menentukan beberapa titik bantu lainnya (jika di perlukan)

FUNGSI KUADRAT

Examples :1. If the function Y = 2x+3x- m have the minimum of the value of Y is 1

. How many the value of m ?The anwer is :

(The minimum of the value of is b raised to the power of two minus four multiplied by a multliplied by c dividied by negative four multliplied by a)

(Negative one five over eight is three raised to the power of two minus four multliplied by two multliplied by negative a half m dividied by negative four multliplied by two )

Negative thirteen multliplied by negative eight is eight multliplied by nine plus four mThirteen is nine plus four mThirteen minus nine is four mNegative thirteen over eight is nine plus four m dividied by negative eight Four is four mOne is mThe conclusion : the value of m is one 2. How the value of point of intersection from graphic kuadran funtion Y = x - 4x 5 ?The answer is

Point of intersection with axis of the abscis (y = 0)

The value of x raised to the power of two minus four the value of x minus five is zero The value of x plus one multlplied by the value of x minus five is zeroThe value of The value of

is negative oneis five

Then,point of intersection with axis of the abscis (y=0) is (-1,0) and (5,0)Point of intersection with axis of the ordinate (x = 0)

The value of Y is the value of x raised to the power of two minus four the value of x minus fiveThe value of Y is zero raised to the power of two minus four multliplied by zero multliplied by negative fiveThe value of Y is negative fiveThen, point of intersection with axis of the ordinat is (x=0) is (0,-5)TERIMA KASIH