Quadratics & PolynomialsCompleting the square, vertex form, the factoring patterns and…10th GradeCOMPLETING THE SQUAREx² + 6x + 5 = 01. Move the constant: x² + 6x = −52. Add (b/2)² = 9 to both sides: x² + 6x + 9 = 43. Factor: (x + 3)² = 4 → x + 3 = ±2 → x = −1 or −5VERTEX FORMy = a(x − h)² + k → vertex (h, k)a > 0 opens up (minimum). a < 0 opens down (maximum).From standard form, the axis of symmetry is x = −b / 2a. Substitute to get k.FACTORING PATTERNSDifference of squaresa² − b² = (a + b)(a − b)x² − 16 = (x+4)(x−4)Perfect square trinomiala² ± 2ab + b² = (a ± b)²x² + 10x + 25 = (x+5)²Sum of cubesa³ + b³ = (a+b)(a² − ab + b²)x³ + 8Difference of cubesa³ − b³ = (a−b)(a² + ab + b²)x³ − 27Groupingax + ay + bx + by = (a+b)(x+y)four termsEnd behavior: even degree → both ends together. Odd degree → ends opposite.Leading coefficient positive → right end rises.Quadratics & Polynomialswww.littleactivity.com

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Math · 10th Grade

Quadratics & Polynomials

Completing the square, vertex form, the factoring patterns and end behaviour.

How to use it

The summary sheet for the algebra posters in this set.

Free · print-ready PDF · US Letter and A4

Grade
10th Grade
Ages
15–16
Subject
Math
Pages
1

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