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Transcript
REMINDER: Expressions versus Equations Simplify: 2 3x x 4 Solve: 2 3x x 4 =2 POLYNOMIALS: Take the form: Where “ai” (the coefficient) is a number in some number system and “n” is a non-negative integer. If a0 ≠ 0 then the polynomial is referred to as a polynomial of degree n. Examples: 3x + 4 is a polynomial of degree 1 (Linear) 3x2 + x – 2 is a polynomial of degree 2 (Quadratic) x6 + 4x5 – 2x2 + 3x +7 is a polynomial of degree 6 Linear Equations Examples : y = 3x +4 1 x3 f(x) = 3 1 what about: y = 3 x 3 ?? 1 1 this can be re-written as y = 3 x 3 where the exponent is a negative number…thus it is NOT a polynomial. A linear equation takes one of two forms: The slope/y-intercept form…………..y = mx + b The x and y represent any point on that line, the point (x,y) The m represents the gradient (slope) of the line B represents the y intercept (value of y when x=0) The general equation of a line………Ax + By + C = 0 A, B, C are parameters. (difference between a parameter and a variable???) (x,y) any point on the line The slope of this line is represented by A B To find the y intercept let x =0, solve for y To find the x interecept let y = 0, solve for x Graphing a Linear Equation. Easiest to do by setting the equation in slope/y-intercept form. Y = mx+b…………..first plot the value of b then use the slope to generate other points. Slope = rise y 2 y1 run x2 x1 Deriving the equation of a line. You must have at least one known point on that line and its slope. Given… - 2 points - 1 point and the slope - The equation of a line parallel or perpendicular to the line AND one point on the line you are trying to determine the equation of.