f(x) = 5x^2 + 3x - 14
This is a parabola that opens upward.......the y coordinate of the vertex will be the minimum value
The x coordinate of the vertex = - 3 /(2 * 5 ) = -3/10
Putting this into the polynomial and evaluting we have that
5 (-3/10)^2 + 3(-3/10) - `14 =
45/100 - 9/10 - 14 =
9/20 - 18/20 - 280/20 =
-289/ 20 = the minimum