Quadratic Equations
An example of a Quadratic Equation:
The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x^2).
It is also called an "Equation of Degree 2" (because of the "2" on the x)
The Standard Form of a Quadratic Equation looks like this:
In this one a=2, b=5 and c=3 This one is a little more tricky:
ax2 + bx + c = 0
But sometimes a quadratic equation doesn't look like that! For example:
In disguise → In Standard Form a, b and c x^2 = 3x -1 Move all terms to left hand side x2 - 3x + 1 = 0 a=1, b=-3, c=1 2(w2 - 2w) = 5 Expand (undo the brackets),
and move 5 to left 2w^2 - 4w - 5 = 0 a=2, b=-4, c=-5 z(z-1) = 3 Expand, and move 3 to left z2 - z - 3 = 0 a=1, b=-1, c=-3 5 + 1/x - 1/x2 = 0 Multiply by x2
5x2 + x - 1 = 0 a=5, b=1, c=-1
http://www.mathsisfun.com/algebra/quadratic-equation.html
http://www.purplemath.com/modules/solvquad.htm
An example of a Quadratic Equation:
The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x^2).
It is also called an "Equation of Degree 2" (because of the "2" on the x)
The Standard Form of a Quadratic Equation looks like this:
- a, b and c are known values. a can't be 0.
- "x" is the variable or unknown (you don't know it yet).
In this one a=2, b=5 and c=3 This one is a little more tricky:
- Where is a? In fact a=1, as we don't usually write "1x2"
- b = -3
- And where is c? Well, c=0, so is not shown.
ax2 + bx + c = 0
But sometimes a quadratic equation doesn't look like that! For example:
In disguise → In Standard Form a, b and c x^2 = 3x -1 Move all terms to left hand side x2 - 3x + 1 = 0 a=1, b=-3, c=1 2(w2 - 2w) = 5 Expand (undo the brackets),
and move 5 to left 2w^2 - 4w - 5 = 0 a=2, b=-4, c=-5 z(z-1) = 3 Expand, and move 3 to left z2 - z - 3 = 0 a=1, b=-1, c=-3 5 + 1/x - 1/x2 = 0 Multiply by x2
5x2 + x - 1 = 0 a=5, b=1, c=-1
http://www.mathsisfun.com/algebra/quadratic-equation.html
http://www.purplemath.com/modules/solvquad.htm