Question

Determinar las coordenadas del vértice F(x)=-2x²+5x+40

Answer 1

$Vertice =( Xv; Yv) \\ \\ Xv= \frac{-b}{2a} \ siendo \ a = -2 \ b= 5 \\ \\ Xv= \frac{-5}{2(-2)} \\ \\ Xv= \frac{-5}{-4} \\ \\ \boxed{Xv= \frac{5}{4}} \\ \\ \\ Yv= -2x^2 + 5x +40 \ reemplazo \ Xv \\ \\ Yv= -2( \frac{5}{4})^2 + 5( \frac{5}{4}) +40 \\ \\ Yv= -2( \frac{25}{16}) + \frac{25}{4} +40 \\ \\ Yv= \frac{-25}{8} + \frac{25}{4} +40 \\ \\ \boxed{Yv= \frac{345}{8}} \\ \\ (Xv, Yv) \rightarrow ( \frac{5}{4}; \frac{345}{8})$

Espero que te sirva, salu2!!!!