Mathematics · Grades 10–12
Quadratics: solving and graphing
A focused reference to use alongside your practice.
Quadratic formula
Use ax² + bx + c = 0 with a ≠ 0. Real solutions require a non-negative discriminant.
x = (−b ± √(b² − 4ac))/(2a)
x² − 5x + 6 = 0 → x = (5 ± 1)/2 → x = 2 or 3
Vertex form
Positive a opens upward; negative a opens downward.
y = a(x − h)² + k; vertex (h,k)
y = 2(x − 3)² + 1 → vertex (3,1)
Sum and product of roots
These identities apply to the two roots counted with multiplicity, including complex roots.
r₁ + r₂ = −b/a; r₁r₂ = c/a
2 and 3 → sum 5, product 6
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.