Quadratic functions fx can be written in three forms.
Factored form, the product of a constant and two linear terms:
a⋅x−p⋅x−q or a⋅x−p2
The parameters p and q are the roots of the function (the x-intercepts of the graph y=fx). 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:
a x2+b x+c
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:
The vertex of the graph is located at the point h, k. 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.
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