Year 9 - Quadratics - Free practice
Year 9 Quadratics Worksheets & Practice Tests
Graphing parabolas, null factor law, solving quadratic equations.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 9 is when students meet quadratics properly. These worksheets give your student varied practice across graphing parabolas, using the null factor law, and solving monic quadratics with integer roots - the exact skills VCAA tests at the Year 9 level.
What's covered
Sub-skills your student will practise
- ✓Recognising the standard parabola y = x^2
- ✓Effect of transformations on a parabola (y = ax^2 + c)
- ✓Solving quadratic equations by null factor law
- ✓Reading roots from a graph
- ✓Setting up a quadratic from a worded scenario
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Frequently asked
Questions parents ask about quadratics
What's a quadratic function?
A function where the highest power of x is 2 - so y = x^2, y = x^2 + 3x, y = 2x^2 - 5x + 1. Their graphs are always parabolas (U-shaped or upside-down U).
What's the null factor law?
If two things multiply to zero, at least one of them must be zero. So if (x - 3)(x + 5) = 0, then either x - 3 = 0 or x + 5 = 0. This is the main method Year 9 uses to solve quadratics.
How do students sketch a parabola?
Find the y-intercept (set x = 0), the x-intercepts if they exist (set y = 0 and solve), and the vertex (the turning point). Mark those points and draw a smooth curve.
What kind of quadratics does Year 9 solve?
Monic quadratics (where the x^2 coefficient is 1) with integer roots, using null factor law after factorising. Quadratic formula and completing the square arrive in Year 10.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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