Standard Form

$ f(x) = $ a $ x^2 $ b $x $ c

Completed Square Form (Vertex Form)

$ f(x) = $ a $ (\ x $ - h $)^2 $ + k

$ x_{1} $

$ x_{2} $

Discriminant = b² - 4ac

Quadratic Equation Graph

Step by step solution using Quadratic Formula

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

Step by step solution using Completing the Square Method

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

Additional Information

Discriminant

$$ b^2 - 4ac $$

y-Intercept

The point where the quadratic curve cuts the y-axis

$$ (0, c) $$

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

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

if $ a \gt 0 $, quadratic curve will have minimum value and parabola opens up

if $ a \lt 0 $, quadratic curve will have maximum value and parabola opens down

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

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