Question

Definir ponto mínimo ou ponto máximo e dê as coordenadas desse ponto.
a) y=3x²+6x
b) y=-x²+9
c)y=5x²-8x+3

Answer 1

Ym: Valor máximo da função
Xm: Valor mínimo da Função

$Ym=\frac{-\Delta}{4a}\\Xv=\frac{-b}{2a}$

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$a)\\\\y=3x^2+6x\\Ym=\frac{-\Delta}{4a}=\frac{-(36-4.3.0)}{4.3}=\frac{-36}{4}=-9\\\\Xm=\frac{-b}{2a}=\frac{-6}{2.3}=-1\\\\\boxed{P(-1,-9)}$

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$b)\\\\y=-x^2+9\\Ym=\frac{-\Delta}{4a}=\frac{0}{4.-1}=0\\\\Xm=\frac{-b}{2a}=\frac{0}{2.-1}=0\\\\\boxed{P(0,0)}$

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$c)\\\\y=5x^2-8x+3\\\\Ym=\frac{-\Delta}{4a}=\frac{-(64-4.5.3)}{4.5}=\frac{-4}{4.5}=\frac{-1}{5}\\\\<u>Xm</u>=\frac{-b}{2a}=\frac{8}{2.5}=\frac{4}{5}\\\\\boxed{P(\frac{4}{5},\frac{-1}{5})}$