y = 2x2 + x – 3 Without drawing the graph of the equation, 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

Question

y = 2x2 + x – 3  Without drawing the graph of the equation, 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

blank · Answer

The vertex is below the x-axis. There are two points in common with the x-axis.

anonymous · Answer

okay, thanks. do you know this? Calculate the discriminant and use it to determine how many real-number roots the equation has.

3x2 – 6x + 4 = 0

blank · Answer

Discriminant is -12

anonymous · Answer

how many real roots?

blank · Answer

There are no real roots. There is two complex solutions: x=(3+i sqrt(3))/(3),(3-i sqrt(3))/(3)

anonymous · Answer

x2 – x – 2 = 0 is the discriminant for this 7 or -7?

blank · Answer

The discriminant for that one is actually 9. Proof: http://www.wolframalpha.com/input/?i=x2+%E2%80%93+x+%E2%80%93+2+%3D+0+find+discriminant

anonymous · Answer

I had no idea you could just type find the discriminant in there hahaha you just changed my life

blank · Answer

:)