y=x^2+4x-6
axis, vertex, roots
The roots are found by setting y = 0 and completing the square.
x^2 + 4x - 6 = 0
x^2 + 4x = 6
x^2 + 4x + 2^2 = 6 + 2^2 add the square of (1/2) * b, the x coefficient
x^2 + 4x + 2^2 = 6 + 4 + 10
(x + 2) * (x + 2) = 10
x + 2 = ±√10
x + 2 = ±3.16228
x = ±3.16228 - 2
x = 3.16228 - 2 and x = -3.16228 - 2
x = 1.6228 and x = -5.16228
The roots, where the plot crosses the x axis, are (-5.16228, 0) and (1.6228, 0)
For the vertex, x = (-b/2a), and y = -(b^2 - 4ac)/4a
x = (-4/(2*1))
x = -4/2
x = -2
y = -(b^2 - 4ac)/4a
y = -(4^2 - 4(1)(-6))/4(1)
y = -(16 + 24)/4
y = -40/4
y = -10
The vertex is (-2, -10)
The axis is the vertical line x = -2