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133 lines
6.1 KiB
HTML
133 lines
6.1 KiB
HTML
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<title>Finding Intercepts From an Equation</title>
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<h1 align="center">Finding Intercepts From an Equation</h1>
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<p align="center"> </p>
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<div class="def">
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<p><b>X Intercept</b>: where the graph of an equation crosses the x-axis</p>
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<p><b>Y Intercept</b>: where the graph of an equation crosses the y-axis</p>
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</div>
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<p align="center"><img src="images/graph-intercepts.svg" alt="x and y intercepts" /></p>
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<p>To find the intercepts:</p>
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<div class="dotpoint">
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<p>When you want the <b>x intercepts</b> (x,0):</p>
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<p align="center" class="larger">Set y=0 then solve for x</p>
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</div>
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<div class="dotpoint">
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<p>When you want the <b>y intercepts</b> (0,y):</p>
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<p align="center" class="larger">Set x=0 then solve for y</p>
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</div>
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<p> </p>
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<div class="example">
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<h3>Example: Find the intercepts of y = x<sup>2</sup> − 4</h3>
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<p><b>x intercept: set y=0</b></p>
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<p align="center" class="larger">0 = x<sup>2</sup> − 4</p>
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<p align="center" class="larger">x<sup>2</sup> = 4</p>
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<p align="center" class="larger">x = <b>2</b> or <b>−2</b></p>
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<p align="center">The points are <b>(2,0)</b> and <b>(−2,0)</b></p>
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<p><b></b></p>
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<p><b>y intercept: set x=0</b></p>
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<p align="center" class="larger">y = 0<sup>2 </sup>− 4</p>
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<p align="center" class="larger">y = <b>−4</b></p>
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<p align="center">The point is <b>(0,-4)</b></p>
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<p align="center" class="larger"> </p>
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<p>And here is the <a href="../data/function-graphercf00.html?func1=x^2-4&xmin=-12&xmax=12&ymin=-8&ymax=8">graph of x<sup>2</sup> - 4</a> to confirm what we found:</p>
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<p align="center"><img src="images/graph-x2-m4.gif" alt="y = x^2 - 4" width="201" height="199" /></p>
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</div>
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<div class="example">
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<h3>Example: Find the intercepts of x<sup>2 </sup>− 5x + y<sup>2 </sup>+ 3y = 0 </h3>
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<p><b>x intercept: set y=0</b></p>
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<p align="center" class="larger">x<sup>2 </sup>− 5x + 0<sup> </sup>+ 0 = 0 </p>
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<p align="center" class="larger">x(x−5) = 0</p>
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<p align="center" class="larger">x = <b>0</b> and <b>5</b></p>
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<p align="center">The points are <b>(0,0)</b> and <b>(5,0)</b></p>
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<p><b>y intercept: set x=0</b></p>
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<p align="center" class="larger">0<sup> </sup>− 0 + y<sup>2 </sup>+ 3y = 0 </p>
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<p align="center" class="larger">y(y+3) = 0 </p>
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<p align="center" class="larger">y = <b>0</b> or <b>−3</b></p>
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<p align="center">The points are <b>(0,0)</b> and <b>(0,−3)</b></p>
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<p> </p>
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<p>So there are a total of 3 points:</p>
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<p align="center" class="larger">(0,0), (5,0) and (0, −3)</p>
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<p> </p>
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<p>And here is the graph ... it's a circle!</p>
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<p align="center"><img src="images/graph-x2-m5x-y2-p3y.gif" alt="y = x^2 - 4" width="162" height="146" /></p>
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</div>
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<p> </p>
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<div class="related"><a href="index.html">Algebra Index</a></div>
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