The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=4$, what is the largest possible integral value of $b$?
+129895 y =ax^2 + bx - 6
a^2 = 4
If this lies completely below the x axis, then a must be negative because the parabola will turn downward
So....a^2 =4 and a = -2
Since this lies below the x axis it will have no real roots....therefore, the discriminant must be < 0
b^2 - 4(-2)(-6) < 0
b^2 -48 < 0
b^2 < 48
b < 7 → the largest value of b = 6
