Vertex of the parabola y = x² - 4x + 1

For the parabola y = x² - 4x + 1, find the coordinates of the vertex.

Step-by-step

1. x = −b / (2a) = 4 / 2 = 2
   Vertex x-coordinate of the parabola: x = −b/(2a)
2. y = 1×2² + -4×2 + 1 = -3
   Substitute back to get the vertex y-coordinate

Why it works

The vertex of a parabola lies on its axis of symmetry; its x-coordinate is -b/(2a), and substituting that value back into the equation gives the y-coordinate.

Common mistakes

• Dropping the minus sign in x = -b/(2a) and getting x = -2.
• Stopping at the x-coordinate without substituting it back to find y.

Related

parabola-vertex tangent-line parabola-vertex-x2-8x-10