To get really good at quadratic equations in Year 8, students can learn about three main methods: factoring, completing the square, and using the quadratic formula. Here are some fun practice problems for each method.

Factoring

1. Solve ( x^2 - 5x + 6 = 0 ).
2. Factor and solve ( x^2 + 7x + 10 = 0 ).

Completing the Square

1. Solve ( x^2 + 4x - 5 = 0 ) by completing the square.
2. Change ( x^2 - 6x + 8 = 0 ) into completed square form and solve it.

Quadratic Formula

1. Use the quadratic formula on ( 2x^2 + 4x - 6 = 0 ). Here, ( a = 2 ), ( b = 4 ), and ( c = -6 ).
2. Solve ( 3x^2 + 12x + 9 = 0 ) using the formula: [ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

Statistics

Research shows that if students practice 10 to 15 problems for each method, they can improve their understanding by over 30%.

Regular practice helps build confidence, so students can master quadratic equations in different ways. Enjoy practicing!