A.6.15.2 A Whole New Form

Here are two sets of equations for quadratic functions. [br][br]In each column, the expressions that define the output are equivalent.[br]f(x) = g(x) = h(x) and p(x) = q(x) = r(x)[br][br]You may recognize 2 of the forms; the first row is standard form and the second row is factored form.[br]The third row is a new form for today![br][br][img]data:image/png;base64,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[/img][br][br]The expression that defines h is written in vertex form. We can show that it is equivalent to[br]the expression defining by expanding the expression:[br][img]data:image/png;base64,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[/img][br][br]Show that the expressions defining p(x), q(x), and r(x) are equivalent by multiplying out r(x).
Here are graphs representing the quadratic functions, they are written in [b][u]vertex[/u][/b] form.[br]Vertex form contains the vertex (the point on the parabola that lies on the line of symmetry of the parabola - or what you can think of as the "middle" point). [br][br]Notice the [b]x-value[/b] is subtracted from x in the equation, so it has the opposite sign of the vertex.[br]The y-value of the vertex has the same sign in the vertex point as in the equation.[br][br] Vertex is the point (-2, -4)       Vertex is the point (3, 4)[br][img]data:image/png;base64,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[/img] 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[/img]
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Information: A.6.15.2 A Whole New Form