Question

Determine as coordenadas do vértice das funções abaixo e dê a resposta na forma do par ordenado (Xv,Yv).
g(t)=6t²-7t+1
f(x)=[(x-2)(x+7)]-2x

Answer 1

Respostas:

$g(t) = Minimo( \frac{7}{12}, -\frac{25}{24})$

$f(x) = Minimo (-\frac{3}{2}, -\frac{65}{4})$

Explicação passo-a-passo:

$Xv= \frac{-b}{2a}$   -------------    $Yv= \frac{-Delta}{4a}$     ---------------  Δ=b²-4.a.c

• g(t)= 6t²-7t+1

$Delta =( -7)^{2} -4.6.1\\Delta =49-24 \\Delta = 25$      $Xv=\frac{ -(-7)}{2.6}\\\\Xv= \frac{7}{12}$        $Yv= \frac{-25}{4.6} \\\\Yv=\frac{-25}{24}$

• f(x)=[(x-2)(x+7)]-2x  

                         

$y=ax^{2} +bx+c\\y= [(x-2)(x+7)]-2x\\y= x^{2} +7x-2x-14-2x\\y= x^{2} +3x-14$   $Delta =( 3)^{2} -4.1.(-14)\\Delta =9+56 \\Delta = 65$      $Xv=-\frac{(3)}{2.1}\\\\Xv= -\frac{3}{2}$

$Yv= -\frac{(65)}{4.1} \\\\Yv=-\frac{65}{4}$