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Methods3 types of functions1

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Methods3 types of functions1

  1. 1. Maths MethodsTypes of Functions 1
  2. 2. Types of Functions 1Quadratic functions Polynomial functions of degree 2 General quadratic equation is: f(x)=ax2+bx+cThe discriminant, ∆ =b2-4ac, determines thenumber of x-intercepts on a quadratic graph <0, none; =0, one; >0, two
  3. 3. Types of FunctionsYou can use the quadratic formula to find x-intercepts:Quadratic formula:The equation of the axis of symmetry is x= -b/2aThe turning point is (-b/2a, c-(b2/4a))
  4. 4. Types of FunctionsThe factorised form of the quadratic functionis: f(x)=a(x-b)(x-c) x-intercepts are at: (b,0) and (c,0) y-intercepts is: a x -b x -c The turning point is halfway between the x- intercepts If a>0 minimum Turning Point If a<0 maximum Turning Point
  5. 5. Types of FunctionsCubic functions: Polynomials of degree 3 General cubic equation is: f(x)= ax3+bx2+cx+d If a>0, the graph is positive If a<0, the graph is negative
  6. 6. Types of FunctionsFactorised forms of cubic equations: y=a(x-b)(x-c)(x-d) a is the dilation from the x-axis b,c, and d are the x-intercepts If a<0, the graph is reflected about the x-axis
  7. 7. Types of FunctionsFactorised forms of cubic equations: y=(x-b)2(x-c) a is the dilation from the x-axis b and c are the x-intercepts b is the x-intercept and the x-coordinate of the turning point
  8. 8. Types of FunctionsPower form of cubic equations: y=(x-b)3 b is the x-intercept and the x-coordinate of the point of inflection
  9. 9. Types of FunctionsQuartic functions: Polynomials of degree 4 General quartic equation: f(x)=ax4+bx3+cx2+dx+e a>0, the graph is positive a<0, the graph is negative
  10. 10. Types of FunctionsQuartic functions in factorised form: f(x)=a(x-b)(x-c)(x-d)(x-e) x-intercepts at x=b,c,d and e
  11. 11. Types of FunctionsQuartic functions in factorised form: f(x)= a(x – b)(x – c)(x – d)(x – e) x-intercepts at b, c, d and e f(x)=a(x – b)(x – c)3 Cubed factor (x – c)3 shows stationary point of inflection at x=c f(x)=a(x – b)2(x – c)2 Repeated factors (x – b)2 and (x – c)2 show stationary points at x=b and x=c f(x)=ax2(x – b)(x – c) Repeated factor x2 indicates a stationary point at x=0

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