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FACTORISING AND QUADRATIC GRAPHS

FACTORISING AND QUADRATIC GRAPHS. The solutions to any quadratic equation are easily related to their underlying graphs. y. i) Solve the equation x 2 ‒ 2 x ‒ 8 = 0. ( x + 2)( x ‒ 4) = 0. x = ‒2 or x = 4 . x. ii) The graph of y = x 2 ‒ 2 x ‒ 8.

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FACTORISING AND QUADRATIC GRAPHS

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  1. FACTORISING AND QUADRATIC GRAPHS

  2. The solutions to any quadratic equation are easily related to their underlying graphs. y i) Solve the equation x2 ‒ 2x ‒ 8 = 0 (x + 2)(x ‒ 4) = 0 x = ‒2 or x = 4 x ii) The graph of y = x2 ‒ 2x ‒ 8 7 0 5 8 98 5 0 7

  3. And again…… y i) Solve the equation x2 + 2x ‒ 3 = 0 (x + 3)(x ‒ 1) = 0 x = ‒3 or x = 1 ii) The graph of y = x2 + 2x ‒ 3 0 34 3 0 5 12 x

  4. Now to apply our work to sketch graphs…… y i) Solve the equation 2x2 ‒ x ‒ 6 = 0 (2x + 3)(x ‒ 2) = 0 x = ‒1.5 or x = 2 ii) The graph of y = 2x2 ‒ x ‒ 6 x 2 1.5 2 0 1.5 0 0 6 6

  5. And again…… y i) Solve the equation 2x2 + 3x ‒ 5 = 0 (2x + 5)(x ‒ 1) = 0 x = ‒2.5 or x = 1 ii) The graph of y = 2x2 + 3x ‒ 5 1 x 2.5 1 0 2.5 0 0 5 5

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