Parabola uchining koordinatalarini toping (24 – 26):
24. (Og`zaki.)
1) y = (x – 3)2 – 2; 2) y = (x + 4)2 + 3;
3) y = 5(x + 2)2 – 7; 4) y = – 4(x – 1)2 + 5.
25. 1) y = x2 + 4x + 1; 2) y = x2 – 6x – 7;
3) y = 2x2 – 6x + 11; 4) y = –3x2 + 18x – 7.
26. 1) y = x2 + 2; 2) y = –x2 – 5;
3) y = 3x2 + 2x; 4) y = –4x2 + x.
27. Ox o`qida shunday nuqta topingki, undan parabolaning simmetriya o`qi o`tsin:
1) y = x2 + 3; 2) y = (x + 2)2; 3) y = –3(x + 2)2 + 2;
4) y = (x – 2)2 + 2; 5) y = x2 + x + 1; 6) y = 2x2 – 3x + 5.
28. y = x2 – 10x parabolaning o`qi: 1) (5; 10); 2) (3; –8); 3) (5; 0); 4) (–5; 1) nuqtadan o`tadimi?
29. Parabolaning koordinata o`qlari bilan kesishish nuqtalarining koordinatalarini toping:
1) y = x2 – 3x + 2; 2) y = –2x2 + 3x – 1;
3) y = 3x2 – 7x + 12; 4) y = 3x2 – 4x.
30. Agar parabolaning (–1; 6) nuqta orqali o`tishi va uning uchi (1; 2) nuqta ekanligi ma’lum bo`lsa, parabolaning tenglamasini tuzing.
31. (Og`zaki.) (1; –6) nuqta y = –3x2 + 4x – 7 parabolaga tegishli bo`ladimi?
32. Agar (–1; 2) nuqta: 1) y = kx2 + 3x – 4; 2) y = –2x2 + kx – 6 parabolaga tegishli bo`lsa, k ning qiymatini toping.
33. y = x2 parabola andazasi yordamida funksiyaning grafigini yasang:
1) y = (x + 2)2; 2) y = (x + 2)2; 3) y = x2 – 2;
4) y = –x2 + 1; 5) y = – (x – 1)2 – 3; 6) y = (x + 2)2+1.
34. y = 2x2 paraboladan uni:
1) Ox o`qi bo`yicha 3 birlik o`ngga siljitish;
2) Oy o`qi bo`yicha 4 birlik yuqoriga siljitish;
3) Ox o`qi bo`yicha 2 birlik chapga va keyin Oy o`qi bo`yicha bir bielik pastga siljitish;
4) Ox o`qi bo`yicha 1,5 birlik o`ngga va keyin Oy o`qi bo`yicha 3,5 birlik yuqoriga siljitish
natijasida hosil bo`lgan parabolaning tenglamasini yozing.