AC9M9A04Year 9AlgebraPractised on site

AC9M9A04 — Year 9 Algebra

Official Curriculum Content Description:

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

Worked Examples (2)

Example 1Graphing Quadratics & Parabolas
Does the parabola y=−2x2+8x−2y = -2x^2 + 8x - 2 open upwards (concave up, with a minimum) or downwards (concave down, with a maximum)?
Common mistake: Confusing the sign of the leading coefficient with the direction of opening.
Correct Answer:downwards
Worked Solution:
1. Look at the leading coefficient aa in y=−2x2+8x−2y = -2x^2 + 8x - 2: a=−2a = -2. 2. Since a<0a < 0, the parabola opens downwards.
Example 2Solving Quadratic Equations by Factorising
Solve by factorising: x2+6x−16=0x^2 + 6x - 16 = 0.
Common mistake: Reporting only one solution to the quadratic equation
Correct Answer:x=−8x = -8 or x=2x = 2
Worked Solution:
Factorise into two brackets: (x+8)(x−2)=0(x + 8)(x - 2) = 0 Set each factor to zero to find the roots: x=−8x = -8 or x=2x = 2.

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