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Linear, Non-Linear Equations' Graphs | Linear, Quadratic, Cubic and Reciprocal Graphs Explanation

LINEAR GRAPHS Coordinates are pairs of numbers used to describe the position of a point on a grid. The 1st number is the distance moved along the x-axis. The 2nd number is the distance moved along the y – axis. The x–axis and y–axis cross at the origin, 0 The coordinates (x, y) describe the position of a point x units across, left or right, and y units up or down from the origin. Recognising graphs Linear (Straight Line) graphs General equation y = mx + c; m is the gradient - c is the y- intercept m = change in y/ change in x Quadratic graphs A quadratic graph is produced when you have an equation of the form y=ax^2 ( squared ) +bx+c, where b and c can be zero but 'a' cannot be zero. All quadratic graphs have a line of symmetry. Positive quadratic graphs (where a is greater than 0) are U-shaped and have a turning point at the bottom of the curve. Negative quadratic graphs (where a is less than zero) are ∩-shaped and have a turning point at the top of the curve. Cubic graphs General equation y = ax^3( cubic) + bx^2 (squared) + cx + d a cannot be zero, The graph has rotational symmetry, Points are joined with a smooth curve – The graph crosses the x–axis at one or three points Reciprocal graphs A graph of the form y=1/x is known as a reciprocal graph and once drawn, looks like this: In algebra, letters are used to stand for values that can change (variables ) or for values that are not known ( unknowns ). A term is a number or letter on its own, or numbers and letters multiplied together, Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering. Collecting like terms means simplifying terms in expressions in which the variables are the same. 5 x n and n x 5 are both written 5n a x b and b x a are both written ab 5a, 7a, a, 12a,... are examples of like terms 5a, 7b, z, 12y,..... are examples of unlike terms Collecting like terms means simplifying terms in expressions in which the variables are the same. In the expression 4a + 3b + 3a - 6b, the tears 4a and 3a are like tears, as are 3b and - 6b. The Federal Trade Commission (“FTC”) requires that all affiliate marketing be disclosed. This requirement is part of the FTC’ attempts to make sure that consumers are presented with as much accurate information as possible when making decisions about their purchases. Linear, Non-Linear Equations' Graphs | Linear, Quadratic, Cubic and Reciprocal Graphs Explanation