Математика25 мин

Quadratic Functions

Three forms of a quadratic, the discriminant, and the quadratic formula — when to use which.

Three forms

Convert between forms by completing the square or expanding. Each form makes a different question easy.

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\Delta = b^2 - 4ac

The discriminant.

Solve

Solve $2x^2 - 5x + 3 = 0$ .

Жауап: $x = 1$ or $x = 3/2$

x_{vertex} = -\dfrac{b}{2a},\quad y_{vertex} = c - \dfrac{b^2}{4a}

Жаттығу

Find the vertex of $y = x^2 - 6x + 5$ .

Жауап пен түсініктемені көру

Жауап: $(3, -4)$

$x = 6/2 = 3$ , $y = 9 - 18 + 5 = -4$ .