In that example, 1 is added to both sides of the original equation.) “Are the original equation \((x-5)(x-3)=\text-1\) and the rewritten one \((x-5)(x-3)+1=0\) equivalent?” (Yes, each pair of equations are equivalent.Invite students to share their responses, graphs, and explanations on how they used the graphs to solve the equations. Graphing \(y=x(x+6)-8\) and examining the \(x\)-intercepts of the graph allow us to see the number of solutions and what they are. In the case of \(x(x+6)-8=0\), the function whose zeros we want to find is defined by \(x(x+6)-8\). By now, students recognize that when a quadratic equation is in the form of \(\text = 0\) is essentially to find the zeros of a quadratic function defined by that expression, and that the zeros of a function correspond to the horizontal intercepts of its graph.
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