Explanation:
we have 2 unknown variables : b, c
and we have 2 points on the curve that we can use to set up 2 equations to solve for the 2 variables :
0 = 2² +b×2 + c = 4 + 2b + c
-14 = 0² + b×0 + c = c
so, we can use c = -14 in the first equation and get
0 = 4 + 2b - 14 = 2b - 10
10 = 2b
b = 5
so, our function is
y = x² + 5x - 14
the x coordinate of the turning point or vertex of the parabola (if the parabola opens up or down, like in our case here) is
x = -b/2a = -5/(2×1) = -5/2
the x-coordinate of the turning point is -5/2 or -2.5.