Standard Form of a Quadratic

≈ 20 min

A quadratic equation has the standard form

ax^2 + bx + c = 0, \qquad a \neq 0

The highest power of the variable is 2 — that is what makes it quadratic. Identifying $a$ , $b$ and $c$ correctly (signs included!) powers every method to come.

Example. For $3x^2 - 2x + 1 = 0$ : $a = 3$ , $b = -2$ , $c = 1$ .

Rearranging. $x^2 = 5x - 6$ is quadratic but not in standard form. Move everything left:

x^2 - 5x + 6 = 0 \qquad (a = 1,\ b = -5,\ c = 6)

Missing terms are fine: $x^2 - 9 = 0$ has $b = 0$ ; $x^2 + 4x = 0$ has $c = 0$ .

In $2x^2 - 7x + 3 = 0$ , what are $a$ , $b$ and $c$ ?

$a=2,\ b=7,\ c=3$

$a=2,\ b=-7,\ c=3$

$a=-7,\ b=2,\ c=3$

$a=2,\ b=-7,\ c=-3$

Which of these equations is quadratic?

$5x - 3 = 0$

$x^3 - x = 0$

$4x^2 - x + 2 = 0$

$\dfrac{2}{x} + 1 = 0$

What is the value of $a$ in $3x^2 - 2x + 1 = 0$ ?

Rearrange $x^2 = 5x - 6$ into standard form (everything on the left, zero on the right). Answer like x^2-5x+6=0.