PARÁBOLA?

Y = 2x² - x - 15

Encontrando "x" usando :

x = [ - b ± √( b² - 4ac )] / 2a

Donde :

a = 2

b = - 1

c = - 15

x = [ - ( - 1 ) ± √( ( - 1)² - 4(2)( - 15) )] / 2(2)

x = [ 1 ± √( 1 + 120 )] / 4

x = [ 1 ± √( 121 )] / 4

x = ( 1 ± 11 ) / 4

Encontrando "x1" y "x2"

x = ( 1 + 11 ) / 4

x = ( 12 ) / 4

x = 3

x = ( 1 - 11 ) / 4

x = ( - 10 ) / 4

x = - 5 / 2 = - 2.

5

Vértice → x = - b / 2a

x = - ( - 1 ) / 2(2)

x = 1 / 4 = 0.

25

Y( 1 / 4 ) = 2( 1 / 4 )² - ( 1 / 4 ) - 15

Y( 1 / 4 ) = 2( 1 / 16 ) - 61 / 4

Y( 1 / 4 ) = 1 / 8 - 61 / 4 = - 121 / 8 = - 15.

13

Punto del vértice → ( 1 / 4, - 121 / 8 )

¡Espero haberte ayudado, saludos!