Here are some common algebraic formulas

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  1. Quadratic formula: x = [-b ± √(b^2 - 4ac)] / 2a, where ax^2 + bx + c = 0
  2. Distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of two points in a plane
  3. Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of two points in a plane
  4. Slope formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on a line
  5. Point-slope formula: y - y1 = m(x - x1), where (x1, y1) is a point on a line and m is the slope of the line
  6. Slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept
  7. Standard form of a line: Ax + By = C, where A, B, and C are constants
  8. Exponential growth formula: A = P(1 + r/n)^(nt), where A is the amount after t years, P is the initial amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years
  9. Exponential decay formula: A = P(1 - r/n)^(nt), where A is the amount after t years, P is the initial amount, r is the annual decay rate, n is the number of times decay occurs per year, and t is the number of years
  10. Logarithm rules: log (xy) = log x + log y, log (x/y) = log x - log y, log x^n = n log x, where x, y, and n are positive numbers and log is the logarithm with base 10 or base e.

These formulas are used in various fields, such as mathematics, science, engineering, and finance, among others. Knowing and understanding these formulas can help in solving problems and making calculations more efficiently.

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