Urgenteee graficar y = 2x ^ 2 + 9x - 5?

Y = 2X² + 9X - 5

Hacemos Y = 0 para hallar los punto de corte en eje X

0 = 2X² + 9X - 5

Donde : a = 2 ; b = 9 ; c = - 5

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-9%5Cpm%20%5Csqrt%7B9%5E2-4%282%29%28-5%29%7D%7D%7B2%282%29%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-9%5Cpm%20%5Csqrt%7B81%2B40%7D%7D%7B4%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-9%5Cpm%20%5Csqrt%7B121%7D%7D%7B4%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-9%5Cpm%20%5C%2011%7D%7B4%7D" />

X1 = [ - 9 + 11] / 4 = 2 / 4 = 1 / 2

X2 = [ - 9 - 11] / 4 = - 20 / 4 = - 5

Puntos de corte para el eje X se producen en : (1 / 2 , 0) y ( - 5 , 0)

ahora hallamos el vertice.

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

h = [( - 9) / (2(2))]

h = [ - 9 / 4]

h = - 2.

25

k = [(4ac - b²) / (4a)]

k = [(4(2)( - 5) - (9)²) / (4(2))]

k = [( - 40 - 81) / (8)]

k = [( - 121) / (8)]

k = - 15.

125

Vertice : (h, k) = ( - 2.

25 , - 15.

125)

Te anexo la grafica.