what is the vertex of the parabola

Let's consider the equation of parabola, y = a·(x - α)·(x - β)where α, β are the x-intercepts.From the given graph, the y-intercept is (0, -3).From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.So the equation of parabola would be now, y = a·(x + 1)·(x - 3)We can plug the y-intercept (0, -3) in the equation to find value of 'a'.-3 = a·(0+1)·(0-3)-3 = -3aa = 1So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3Comparing it with y = ax² + bx + cThe x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.Hence, vertex would be (1, -4).