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Graphs equations and tables. External on the 14 th of November 4 credits Thanks to http://www.studyit.org.nz/subjects/maths/math1/3 / http://www.studyit.org.nz/subjects/maths/math1/3 / 2011 Ms Allan

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Mathematics 1.3 Investigate relationships between tables, equations and graphs Linear equations Simultaneous linear equations Linear graphs Linear patterns Graphing parabolas Quadratic equations Quadratic patterns Exponential equations and graphs Interpreting gradients Linear equations Simultaneous linear equations Linear graphs Linear patterns Graphing parabolas Quadratic equations Quadratic patterns Exponential equations and graphs Interpreting gradients

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Linear equations Solve for a,b and c: 3a+6 = 3-4a 3(b + 2) = 15 4c – 9 > c + 7

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Simultaneous linear equations Solve for A and b A = 3b + 2 A = 6b - 8

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Linear graphs Draw these graphs on a set of axis y = 2x + 3 X = 3 Y = 8 Y = -0.5x - 1

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Linear graphs

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Linear patterns For the sequence of diagrams below, find the rule for the number of white tiles (w) in terms of the number of black tiles (b).

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Graphing parabolas Draw these graphs on a set of axis y = x 2 + 3 y = -x 2 + 2 y = (x-4) 2 y = (x+4) 2 + 1

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Graphing parabolas

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Quadratic equations What are the x intercepts of Y=(x-3)(x+4) Solve for x by factorising first 0 = x 2 + 7x + 12

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Quadratic patterns Find a rule for calculating the total number of boxes in each diagram, if the number of boxes in the bottom layer is known. Draw up a table to show the number of boxes in the bottom layer and the total number of boxes in each diagram. Calculate the differences between the terms.

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Exponential equations and graphs Draw the graphs of these equations on an x and y axis. Y=2 x Y=3 x + 2 Y=4 x

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Exponential equations and graphs

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Interpreting gradients Calculate the gradient of the 3 linear graphs. What do these gradients represent?

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Objectives: To identify quadratic functions and graphs and to model data with quadratic functions.

Objectives: To identify quadratic functions and graphs and to model data with quadratic functions.

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