Use of Maths Module- Algebra 4.5 / 5 MathematicsTrigonometry and radiansASAll boards Created by: EmilyCreated on: 13-12-11 09:42 Linear Functions Linear model M and C are constants. The gradient = M The intercept on the y axis = C Gradient = Ystep/ X step Graph mode, Enter equation, Draw, G-Solve = Y intercept 1 of 9 Linear Functions Models of direct proportion Variables X and Y are in direct proportion if Y=kX The graph of Y against X is a STRAIGHT LINE, with gradient k, which passes through the origin (0,0). k often gives a significant measure, e.g for a currency conversion graph k gives the rate of exchange. 2 of 9 Quadratic Functions Quadratic Functions Y=ax²+ bx+c a,b and c are constants. You can make every possible quadratic function by changing the values of a,b and c. Completeing the square gives the form Y=m(x+n)²+ p If m is positive, the function has a minimum value of p, when x=-n. If m is negative, this function has a maximum value of p, when x= -n. 3 of 9 Quadratic Functions Quadratic equations Quadratic equations can be solves by: Using a graph Completing the square Factorising Using the formula x= -b±√ b² - 4ac / 2a Quadratic models can be used to model all or part of a set of data. 4 of 9 Quadratic Functions Quadratic graphs Quadratic graphs have either a single minimum point or a single maximum point. Y= ax²+ bx +c 5 of 9 Quadratic Functions Quadratic graphs Graphs can be used to solve equations by finding the x co-ordinates of the points of intersection with the x axis or other lines. Graph mode, Enter equation, Draw, G-Solve, roots = points of intersection. 6 of 9 Quadratic Functions Roots- The solution when y=0, or the x-axis interception (cross) Zeros- Vertex- Minimum- Lowest value Maximum- Highest value Turning points- Minimum/maximum Line of symmetry- Line of which both sides are symmetrical Y intercept- Point of which the graph crosses the y axes. 7 of 9 Quadratic Functions Real life situation/s: 8 of 9 Trig functions Y=Asin(B(X+C))+D A= Amplitude degrees/B = Period C= phase shift D= vertical shift 9 of 9

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