Mod 1: Algebra & Functions

• Linear equations: these equations are often in the form of, $y =$$mx+$$b$
• A linear equation will always have one x value and one corresponding y value.
• When completing squares:

  1. add the second term by the 1/2 and squared of that term and subtract if it is in the same equation. Take the first term and add/subtract it with the third, new term. Take the third term that you subtracted and subtract it with the ither term since it had no relationship with the first term
  2. If this is in an equation, then simply take the new third term and add it to the other side of the equation
• The quadratic formula is used to find the roots (or solutions) of any quadratic equation in standard form. The general form of a quadratic equation is ax^2 + bx + c = 0 where a, b, and c are constants and a≠0.
• Functions can be linear, quadratic, exponential, polynomials, trigonometric or logarithmic, semi-circular
• A function can be represented by an equation, table, or graph.
• A quadratic function results in a parabolic curve.
• Polynomials: Any even powers to x results in a parabolic function, so it is a bounce and the amount of x-intercepts can range from 0 to 2. Any odd powers to x results in wave and the amount of x-intercepts can range from 1 to 3.
• A linear function has a constant rate of change and produces a straight line graph.
• The vertex is the lowest (minimum point)/highest (maximum point) on the graph.
• The x-intercept is the point where the graph crosses the horizontal axis (x = 0).
• The x-intercepts are where the parabola intersects with the x-axis.
• The axis of symmetry passes through the vertex and divides the parabola into two equal parts, and is only the x value of the parabola, This could be found by $-b/2a$
• Inverse functions have the same domain as their original function but different ranges.
• To find the inverse of a function, switch x and y
• The vertical line test: used to test if a graph is a function or not, since one x value should only have a y value, meanwhile, a y value can have multiple x values.
• 1. To find if a function is even, f(x) = f(-x)
  2. To find if a function is odd, f(-x) = -f(x)
• if discriminant is 0 = one sol

  if discriminant is less than 0 = no sol

  if discriminant is more than 0 = two sol
• When rationalising a denominator, for ex (8/7−√8) be sure to multiply it with a fraction that has the same, conjugate denominator as the example we have, and should equal to 1, so we will multiply this by (7+√8/7+√8)
• $(a^m)^n =$$a^m times^n$

  $x^4•x^3 =$$x^4 +$$^3$

  If it is division, both of the powers are subtracted

  $4^h =$$√4$Where h is 1/2

  $4^m =$$1/4^1$Where m is -1
• There are two ways of solving simultaneous equations:

  1. Elimination
  2. Substitution/making an equation