Find the vertex coordinates of parabola y = 2x^2 - 4x + 1

In this exercise I have to find the coordinates of the vertex of the parabola. Given the general equation y= ax^2 + bx + c , the value of a is 2, the value of b is -4 and the value of c is 1.

In order to compute the x-coordinate, I apply the formula –b/2a and, by substituting the values written before, I have that Vx = -(-4)/(2*2) = 4/4 = 1.

For the y-coordinate, I apply the formula –Δ/4a, where Δ = b^2 – 4ac. By substituting the parameters value into Δ, I obtain Δ = (-4)^2 – 421 = 16 -8 = 8. By plugging it into the general formule, I have Vy = - 8/(4*2) = - 8/8 = - 1. The vertex coordinates are thus (1; - 1).