2: Quadratic Functions

== Key Formulas for Quadratic Functions == === Standard Form === \[ f(x) = ax^2 + bx + c \quad (a \ne 0) $$ === Vertex (x-coordinate) === $$ x = -\frac{b}{2a} $$ === Quadratic Formula === $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$ === Discriminant === $$ D = b^2 - 4ac $$ * If $D > 0$: two real solutions * If $D = 0$: one real solution * If $D < 0$: two complex solutions === Vertex Form === $$ f(x) = a(x - h)^2 + k $$ === Factored Form === $$ f(x) = a(x - r_1)(x - r_2) \]

Figure : An array of satellite dishes. (credit: Matthew Colvin de Valle, Flickr)

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