Degree two is the whole idea
A linear equation like 2x + 3 = 0 has the variable to the first power only. A quadratic equation is one step up: somewhere there is an x^2, and no power higher than two. That single squared term changes everything — the number of solutions, the shape of the graph, the methods you need. The name comes from *quadratus*, Latin for square, because x^2 is literally x times x, the area of a square with side x.
Every quadratic can be tidied into one standard form. Move every term to one side so the other side is zero, combine like terms, and write the powers in descending order. You arrive at the shape that the rest of this track lives inside.
Standard form of a quadratic:
a x^2 + b x + c = 0 with a ≠ 0
Example — tidy 3x^2 = 5x - 2 into standard form:
3x^2 = 5x - 2
3x^2 - 5x = -2 (move 5x left)
3x^2 - 5x + 2 = 0 (move -2 left)
Now a = 3, b = -5, c = 2.What a, b, and c each control
The three numbers a, b, c are the coefficients. Here a is the leading coefficient (it multiplies x^2), b is the coefficient of x, and c is the constant term, the lone number with no variable. Naming them carefully matters, because every formula later feeds on exactly these three values.
Watch out for disguises. The equation x(x + 4) = 7 looks linear until you expand it: x^2 + 4x = 7, then x^2 + 4x - 7 = 0. Likewise 5/x + x = 6 hides a quadratic once you clear the fraction. Always expand and tidy before you decide what kind of equation you are facing.