The graph of the equation y=ax^2+bx-18 is completely below the x axis. If , a^2=49 what is the largest possible integral value of b?
+128406 If this graph is completely below the x axis, then a must = -7
So we have
-7x^2 + bx - 18
And since it lies below the x axis the roots are complex.....so we want to find the largest value of b such that the discriminant is < 0.....so.....
b^2 - 4(-7)(-18) < 0
b^2 - 504 < 0
b^2 < 504
b < floor [sqrt (504)] = 22
So b = 22 is the largest integer balue for b that will guarantee that the function lies nelow the x axis
See the graph here : https://www.desmos.com/calculator/lhbvrcjkmg
