Question

determinar el vertice de cada parabola
b(x)=-5x2
f(x)=-2x+1/3x2
f(x)=x2+x+1

Answer 1

Ecuación de parábola:

ax² + bx + c

Vértice:

x = -b / 2a
y = f(x), el "x" es el encontrado anteriormente!

b(x) = -5x²

x = -b / 2a = - 0 / 2(5) = 0
y = 5(0)² = 0

v = (0,0)

f(x) = -2x + (1/3)x²
f(x) = (1/3)x² - 2x

x = -b / 2a = - (-2) / 2(1/3) = 2/ (2/3) = 3
y = (1/3)(3)² - 2(3) = 3 - 6 = -3

v = (3, -3)

f(x) = x² + x + 1

x = -b / 2a = - 1 / 2(1) = - 1/2
y = ( -1/2 )² + ( -1/2) + 1
y = 1/4 - 1/2 + 1 = 3/4

v = ( -1/2, 3/4 )

Espero haberte ayudado, saludos!