Question

Determine as fórmulas das coordenadas do vértice ( Xv e Yv):

Answer 1

Resposta:

P(x)=ax²+bx+c

ax²+bx+c=0

x'=[-b+√Δ]/2a

x''=[-b-√Δ]/2a

xv= (x'+x'')/2  = {[-b+√Δ]/2a +[-b-√Δ]/2a}/2

xv= [(-2b)/2a]/2 = -b/2a

yv=P(xv)= a*(xv)²+b*xv+c

yv= a*(-b/2a)²+b*(-b/2a)+c

yv= a*(b²/4a²)-b²/2a+c

yv= a*(b²/4a²)-b²*2a/4a²+c *4a²/4a²

yv= (a/4a²)*{ (b²)-b²*2+c *4a}

yv= (-a/4a²)*{ b²-4*a*c}

yv=(-1/4a)*{ Δ}

yv= -Δ/4a