2ac7fb7b-f45d-456f-b9f4-673c90472036.html

<p>Display a series of equations that, prior to this lesson, students could only solve by graphing.</p>
<p>For instance:</p>
<p>\(x^2+3x &minus; 18 = 0\)</p>
<p>\(x^2&minus; 4 = 5x\)</p>
<p>\(x(x &minus; 7) = -6\)</p>
<p>\(2x^2 &minus; 9x + 10 = 0\)</p>
<p>\((x + 6)(x &minus; 6) = 11\)</p>
<p>Ask students to choose an equation that they think they could solve without graphing. Then, ask them to explain to a partner why they believe they could solve the equation.</p>
<p>Consider displaying \((x + 9)(x &minus; 9) = 19\) for all to see and using it as an example: "I think I can solve \((x + 9)(x &minus; 9) = 19\) because I know the expression on the left is equivalent to \(x^2&minus; 9^2\) and I can rewrite the equation as \(x^2 &minus; 81 = 19\), which I can solve by rearranging the terms."</p>
<p>Then, ask if any of the equations appear to be unsolvable other than by graphing and why. Of the equations shown here, \(2x^2&minus; 9x + 10 = 0\) is the only one that students aren&rsquo;t yet equipped to solve because the coefficient of \(x^2\) is not 1. Students will begin looking at such equations in an upcoming lesson.</p>