determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on , or below the x -axis

y=-2x^2+x-3

Answer:

here we can rewrite your function as below:

y = -2 (x +1/4)^2 +25/8

so the vertex is V= (-1/4, 25/8) so it doesn't lie above the x-axis.

Furthermore, the discriminant is:

1 - 4*(-2)*(-3) = 1- 24 = -23

discriminant = -23.

being the discriminant negative, then we have no real solutions or roots

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