Maths_Yr12+GRAPHS

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Draw straight-forward non-linear graphs
//Graphs to be drawn will be from given equations.// //Show features; intercepts, symmetry, maxima or minima (for quadratics), asymptotes//.
 * quadratics that can be factorised or put in the form
 * //y = =// y //±//± //(x – a)2 + b//(x – a)2 + b
 * factorised polynomials (coefficient of //x// n = ±1)
 * rectangular hyperbolae of the form y=a/bx, a,b Î I, b≠0
 * circles with centre at the origin
 * exponential functions of the form //y = ax, a// Î N
 * logarithmic functions of the form //y// = loga//x//, //a// Î N

Draw non-linear graphs

 * rectangular hyperbolae of the form y=(a/(x-c))+b
 * circles of the form (//x// – //a//)2 + (//y// – //b//)2 = //r// 2
 * exponential functions of the form //y// = //a*(//x-b)+c and either b or c equal to zero
 * logarithmic functions of the form //y// =loga//(x - b)+c//, either b or c 0

Use non-linear graphs to solve problems
2. interpreting features.
 * 1) writing equations selected from the following types of graphs:
 * any graphs listed for achievement
 * hyperbola as listed above for merit, where b or c = 0
 * circle as listed above for merit

Determine and apply an appropriate model for a situation involving graphs.
- a situation requiring finding points of intersection - using equations of graphs to solve problems.
 * Writing an equation of a graph will be required and may involve more than one equation, or piecewise function, to describe a situation.
 * The application of a model could include:
 * Polynomials may have coefficients of //x// n other than ±1, and for exponential and logarithmic functions both b and c may have non-zero values.