Standard Form

f (x) =

x^{2}

x

Completed Square Form (Vertex Form)

f (x) =

(x

- h

)^{2}

+ k

x_{1}

x_{2}

Discriminant = b² - 4ac

Quadratic Equation Graph

Step by step solution using Quadratic Formula

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Step by step solution using Completing the Square Method

$(m \pm n)^{2} = m^{2} \pm 2 m n + n^{2}$

Additional Information

Discriminant

$b^{2} - 4 a c$

y-Intercept

The point where the quadratic curve cuts the y-axis

$(0, c)$

$(\frac{- b}{2 a}, \frac{- b^{2}}{4 a} + c)$

$x = \frac{- b}{2 a}$

a > 0

, quadratic curve will have minimum value and parabola opens up

a < 0

, quadratic curve will have maximum value and parabola opens down

$Minimum / Maximum value = \frac{- b^{2}}{4 a} + c$

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