db3b053a-49ae-4b2a-a683-0e14704e270d.html

<p>To help students consolidate the ideas in the lesson, discuss questions such as:</p>
<ul>
  <li>&ldquo;How do you know if the relationship between two quantities represents a quadratic function? What clues would you look for?&rdquo; (There is only one output for every input. In the relationship, one quantity is in some way squared or multiplied by itself to obtain the second quantity. The relationship can be expressed with a squared term, among other ways. A pattern that changes linearly in two directions, such as a rectangle that grows linearly in length and width.) </li>
  <li>&ldquo;What does it mean when we say that two expressions define the same function?&rdquo; (The two expressions describe the same relationship between two quantities, and there&rsquo;s a way to show that this is the case.) </li>
  <li>&ldquo;Can we say that \(x(x+5)\) and \(x^2+5x\) define the same function? How can you show if they do or don&rsquo;t?&rdquo; (Yes. Using the Distributive Property shows that \(x(x+5)=x^2+5x\). A diagram can also show that the two are equivalent. A rectangle with side lengths \(x\) and \(x+5\) has the area \(x(x+5)\). If we decompose the rectangle into two sub-rectangles that are \(x\) by \(x\) and \(x\) by \(5\) and calculate their areas and combine them, we get \(x^2+5x\).) </li>
</ul>