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).
[img]data:image/png;base64,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[/img]