explain both the error in Priya’s argument and the validity of Mai’s argument in terms of the zero product property. In articulating why certain lines of reasoning are correct or incorrect, they practice constructing logical arguments (MP3). Students critique several arguments on how to solve quadratic equations. This activity aims to uncover some common misconceptions in solving quadratic equations and to reinforce that certain familiar moves for solving equations are not effective. (Because students won’t know about numbers that aren’t real until a future course, for now it is sufficient to say “no solutions.”) Likewise, some quadratic equations have two solutions, some have one solution, and some have no real solutions. 
Make sure students understand that some quadratic functions have two zeros, some have one zero, and some have no zeros, so their respective graphs will have two, one, or no horizontal intercepts, respectively.
The zeros correspond to the \(x\)-intercepts of the graph.)
"Why might it be helpful to rearrange the equation so that one side is an expression and the other side is 0?" (It allows us to find the zeros of the function defined by that expression. 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.
0 kommentar(er)
