Quadratics — NSW Year 9 Advanced Maths
Expanding and factorising quadratics, completing the square and solving quadratic equations. Six subtopics and 120 practice questions with fully worked solutions, aligned to NESA outcomes MA5-ALG-P-02 and MA5-EQU-P-01.
Quadratics in NSW Year 9 Advanced
A quadratic expression has a squared term as its highest power, as in \(x^2 - 2x - 24\). In Year 9 Advanced, students expand quadratic expressions, factorise monic and non-monic trinomials and special products, complete the square to factorise expressions that do not factorise neatly, and solve quadratic equations using the fact that a product is zero only when one factor is zero.
The six subtopics below cover expanding quadratic expressions, factorising monic quadratic trinomials, factorising non-monic quadratic trinomials, factorising special binomial products, factorising by completing the square, and solving quadratics by factorising. Quadratics is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Number and Algebra strand (NESA outcomes MA5‑ALG‑C‑01, MA5‑ALG‑P‑01, MA5‑ALG‑P‑02, MA5‑EQU‑P‑01 and MA5‑EQU‑P‑02). It leads on to the quadratic formula and graphing parabolas in Year 10 Advanced.
Subtopics
Quadratics: common questions
How do you expand a perfect square?
Use \((a + b)^2 = a^2 + 2ab + b^2\): square the first term, double the product of the two terms, then square the last term. So \((3x - 4)^2 = 9x^2 - 24x + 16\).
How do you factorise a non-monic quadratic?
Multiply the first and last coefficients, find two numbers with that product that add to the middle coefficient, split the middle term and group in pairs. For \(2x^2 - x - 6\), the product is \(-12\), the numbers are \(-4\) and 3, and the answer is \((x - 2)(2x + 3)\).
What is completing the square?
It rewrites a quadratic as a perfect square plus or minus a number. Since \(x^2 - 8x + 16 = (x - 4)^2\), the expression \(x^2 - 8x + 3 = (x - 4)^2 - 13\).
How do you solve a quadratic equation by factorising?
Rearrange so one side is 0, factorise, then set each factor equal to 0. For \(x^2 + x - 20 = 0\), \((x + 5)(x - 4) = 0\), so \(x = -5\) or \(x = 4\).
Which NESA outcomes cover quadratics in Year 9 Advanced?
Expanding binomial products is MA5‑ALG‑C‑01. Factorising monic trinomials is MA5‑ALG‑P‑01, and special products and non-monic trinomials are MA5‑ALG‑P‑02. Solving monic quadratic equations is MA5‑EQU‑P‑01, and completing the square and non-monic equations are MA5‑EQU‑P‑02.