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Aлгебра 10 обобщение y=ax 2 + bx + c ; a ≠ 0 y=ax 2 + bx ; c = 0 y=ax 2 + c ; b = 0 y=ax 2 ; b = c = 0 Kвадратна функция

Квадратна функция и квадратни неравенства O x y

y=(x – 2)(x + 3)(8x – 3)< 0 X= 2 x= -3 x= ⅜ - + - + -3 ⅜ 2 Xe(- ∞;-3)U( ⅜ ;2)

y=x 3 + 2x 2 – 8x ≥ 0 x(x 2 + 2x – 8)≥ 0 x(x – 2)(x + 4)≥ 0 D=36=6 2 X 1,2 =-2±6 ↓-> -4 2 2 xe[-4;0]U[2;+∞) y=x 4 – 3x 2 – 10 < 0 y=(x - √5)(x + √5)(x 2 +2) y=x 4 + 3x 2 + 3 > 0 D < 0 D= 49 = 7 2 y 1,2 =3 ± 7 ↓ -> 5 2 -2 Xе(-√5;√5)

y=x 3 + 2x 2 – 8x ≥ 0 D=36=6 2 X 1,2 =-2±6 ↓-> -4 2 2 x(x + 2x – 8)≥ 0 x(x – 2)(x + 4)≥ 0 xe(-∞;-3)U( ⅜;2)

Логаритъм a x =b x=log a b a > 0,a ≠ 0,b > 0 n √a k = a Log a a b = b A 0 =1 Log a 1= 0 3 x =4 x=log 3 4 Log 3 3 √27 =log 3 √3 3 = log 3 3 =

Показателни уравнения 7 x2 = 7 5x-6 x 2 = 5x – 6 x 2 – 5x +6 = 0 x 1 = 2 x 2 = 3 4 x+3 =( ⅛) x-1 (2 2 ) x+3 =(2 -3 ) x-1 2 2x+6 =2 -3(x-1) 2x+6=-3(x-1) 2x+6=-3x+3 2x+3x=3-6 5x=-3 x=- 3 / 5 49 x + 5 = 6.7 x 7 2x + 5 = 6.7 x y 2 + 5 = 6y y 2 – 6y + 5 = 0 y 1 =5 y 2 =1 пол.7 x = y 7 x = 5 X 1 = log 7 5 7 x = 1 X 2 =0

Показателни неравенства 36 x < 3 √6 6 2x < 6 1 / 3 2x < 1 / 3 x < 1 / 6 xe (-∞; 1 / 6 ) 0,2 x < 0,04 0,2 x < 0,2 2 x > 2 xe (2;+ ∞)

Приложение Y= ax 2 + bx + c S = S 0 + V 0 t + ½ at 2 S = S 0 + v 0 t - ½ at 2 P = E . I – R 0 . I 2

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