 Factored Form - Maple Help

Factored Form

 Main Concept Quadratic functions $f\left(x\right)$ can be written in three forms.   Factored form, the product of a constant and two linear terms:   $a\cdot \left(x-p\right)\cdot \left(x-q\right)$     or     $a\cdot {\left(x-p\right)}^{2}$   The parameters $p$ and $q$ are the roots of the function (the x-intercepts of the graph $y=f\left(x\right)$). Converting a quadratic function to factored form is called factoring.   Expanded form, a sum of terms, each of which may be a product of a constant and some variables:     The parameter $c$ is the y-intercept, while the parameter $b$ is the slope of the tangent at 0. Converting a quadratic function to expanded form is called expanding.   Standard form, the sum of a constant term, $k$ and a constant, $a$ times the square of a linear term:   $a\cdot {\left(x-h\right)}^{2}+k$   The vertex of the graph is located at the point . Converting a quadratic function to standard form is called completing the square.   In each case the parameter $a$ determines the vertical stretching of the graph.

Choose the two roots of the parabola, and observe how the x-intercepts change to reflect each root.

 a  = p = q = Expanded form: Standard form: Factored form:



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