4.2-bo'lim : Parabolalar
1-18-masalalar uchun quyidagi parabolalarning grafigini chizing. Grafikda cho'qqi, y kesma, x-kesmalar (agar mavjud bo'lsa) va cho'qqining har ikki tomonida kamida bitta nuqta bo'lishi kerak.
- \(f\left( x \right) = - 4{x^2}\)
- \(f\left( x \right) = {\left( {x - 6} \right)^2} + 1\)
- \(f\left( x \right) = {\left( {x + 2} \right)^2} - 4\)
- \(f\left( x \right) = 3{\left( {x - 1} \right)^2} + 12\)
- \(f\left( x \right) = - 6{\left( {x + 5} \right)^2} + 54\)
- \(f\left( x \right) = - {\left( {x - 7} \right)^2} - 3\)
- \(f\left( x \right) = 2{\left( {x + 3} \right)^2} - 6\)
- \(f\left( x \right) = {x^2} - 8\)
- \(f\left( x \right) = - 4{x^2} - 1\)
- \(f\left( x \right) = {x^2} - 16x + 55\)
- \(f\left( x \right) = {x^2} - 2x + 5\)
- \(f\left( x \right) = 4{x^2} + 16x\)
- \(f\left( x \right) = {x^2} + 10x + 25\)
- \(f\left( x \right) = - 2{x^2} + 24x - 64\)
- \(f\left( x \right) = 3{x^2} + 6x - 12\)
- \(f\left( x \right) = - 4{x^2} + 12x - 9\)
- \(f\left( x \right) = - {x^2} + 6x - 16\)
- \(f\left( x \right) = {x^2} + 8x + 5\)
19-25-masalalar uchun quyidagi tenglamalarni \(y = a{\left( {x - h} \right)^2} + k\) ko'rinishiga aylantiring.
- \(f\left( x \right) = {x^2} + 4x\)
- \(f\left( x \right) = {x^2} - 6x + 19\)
- \(f\left( x \right) = - {x^2} + 2x + 6\)
- \(f\left( x \right) = 7{x^2} + 56x + 111\)
- \(f\left( x \right) = 3{x^2} - 60x + 306\)
- \(f\left( x \right) = 25{x^2} + 10x + 1\)
- \(f\left( x \right) = - 2{x^2} - 16x - 18\)