Parabola: vertex and intercepts

For y = x² − 4x + 3, find the vertex, the x-intercepts and the y-intercept.

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 + 3 = -1
   Substitute back to get the vertex y-coordinate
3. Δ = b² − 4ac = 16 − 12 = 4
   The discriminant decides how many times the curve crosses the x-axis
4. x = (4 ± √4) / 2 → 1 and 3
   Quadratic formula
5. x = 0 → y = 3
   The y-intercept is the constant term c

Why it works

The vertex x-coordinate is −b/2a; substituting back gives y. Intercepts come from factorising for x = 0 and setting x = 0 for the y-intercept.

Common mistakes

• Forgetting the minus sign in −b/2a.
• Confusing which intercept is which.

Related

tangent-line similar-triangle-3-4-5-shortest-6 circle-circumference-radius-7