Question

Выделив квадрат двучлена постройте графики функций f(x) = 2x^2 +2x-4f(x)=3x^2-x-5f(x) = 4x^2 -x-2

Answer 1

2·(x²+x-2)=2·(x²+2x·(1/2)+(1/4)-(1/4)-2)=2·((x+(1/2))²-(9/4))

y=2·(x+(1/2))²-(9/2)

Вершина в точке (-1/2; -9/2),ветви вверх

3x²-x-5=3·(x²-(1/3)-(5/3))=3·(x²-2·x·(1/6)+(1/6)²-(1/6)²-(5/3))==3·((x-(1/6))²- (61/36))

y=3(x-(1/6))²-(61/12)

Вершина в точке (1/6; -61/12), ветви вверх

4x²-x-2=2(x²-(1/2)x-2)=2(x²-2x·(1/4)+(1/4)²-(1/4)²-2)=2·((x-(1/4))²-(33/16)

y=2·(x-(1/4))²-(33/8)

Вершина в точке (1/4;-33/8), ветви вверх