f61b0ffd-da36-4232-bbe2-619b6716baf3.html

<p>In this lesson, we saw that quadratic expressions can give us clues about the intercepts of their graphs, and graphs can give us insights about the expressions they represent. Ask students:</p>
<ul>
  <li> &ldquo;If we graph \(y=(x-7)(x-3)\) and \(y=x^2 -10x+21\), will we end up with the same graph? How do you know?&rdquo; (Yes. The two expressions that define y are equivalent. Expanding \((x-7)(x-3)\) gives \(x^2-7x-3x+21\) or \(y=x^2 -10x+21\).) </li>
  <li> &ldquo;Where do you predict the intercepts of the graph will be? How do you make your predictions?&rdquo; (The \(y\)-intercept will be \((0,21)\) and the \(x\)-intercepts will be \((7,0)\) and \((3,0)\). In the examples in the lesson, we saw that the numbers in the factored form give a clue about the \(x\)-intercepts, and the constant term in the standard form gives a clue about the \(y\)-intercept. Also, evaluating \(y\) when \(x=0\) gives us the \(y\)-intercept.) </li>
  <li>&ldquo;What do the \(x\)-intercepts of a graph tell us about the quadratic function it represents?&rdquo; (They tell us the zeros of the function.)</li>
</ul>