Please guys help me with polynomials of graph

<h2>Evaluating a Polynomial For a Given Value</h2>
<p>We have already learned how to evaluate expressions. Since polynomials are expressions, we’ll follow the same procedures to evaluate a <strong>polynomial</strong>. We will substitute the given value for the variable and then simplify using the order of operations.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Evaluate $5{x}^{2}-8x+4$ when</p>
<ol type="1">
<li>$x=4$</li>
<li>$x=-2$</li>
<li>$x=0$</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table summary="This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says “Substitute 4 for x.” The right column contains 5 times 4 squared minus 8 times 4 plus 4. One row down, the left column says “Simplify the exponents.” The right column contains 5 times 16 minus 8 times 4 plus 4. One row down, the left column says “Multiply.” The right column contains 80 minus 32 plus 4. One row down, the left column says “Simplify.” The right column contains 52.">
<tbody>
<tr>
<td>$x=4$</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="5 x squared minus 8 x plus 4." src="https://data.ulearngo.com/assets/52579443-b6a8-4d24-8404-6b42c9682bfd"/></td>
</tr>
<tr>
<td><img alt="Substitute 4 for x." src="https://data.ulearngo.com/assets/581103b2-69e8-4fb2-b1a2-1ab08c3bbf40"/></td>
<td><img alt="5 times 4 squared minus 8 times 4 plus 4." src="https://data.ulearngo.com/assets/55473e1d-ab69-4b11-b65a-82166f4d070a"/></td>
</tr>
<tr>
<td>Simplify the exponents.</td>
<td><img alt="5 times 16 minus 8 times 4 plus 4." src="https://data.ulearngo.com/assets/7fda0987-e1a9-4207-a1e2-982366fd3b85"/></td>
</tr>
<tr>
<td>Multiply.</td>
<td><img alt="80 minus 32 plus 4." src="https://data.ulearngo.com/assets/1a5181b9-26be-4cb7-bc49-d8e8c07e46d2"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="52." src="https://data.ulearngo.com/assets/97790944-5387-4a83-ab9d-b82e68c3296d"/></td>
</tr>
</tbody>
</table>
<table summary="This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says “Substitute negative 2 for x.” The right column contains 5 times negative 2 squared minus 8 times negative 2 plus 4. One row down, the left column says “Simplify the exponents.” The right column contains 5 times 4 minus 8 times negative 2 plus 4. One row down, the left column says “Multiply.” The right column contains 20 plus 16 plus 4. One row down, the left column says “Simplify.” The right column contains 40.">
<tbody>
<tr>
<td>$x=-2$</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="5 x squared minus 8 x plus 4." src="https://data.ulearngo.com/assets/e0149c4d-bc7c-4818-a1c7-a24190a5574e"/></td>
</tr>
<tr>
<td><img alt="Substitute negative 2 for x." src="https://data.ulearngo.com/assets/96add454-b8ba-4d33-8c5b-1e4f92aec70c"/></td>
<td><img alt="5 times negative 2 squared minus 8 times negative 2 plus 4." src="https://data.ulearngo.com/assets/42bf815f-37b1-44f6-98a3-9fb2806d2259"/></td>
</tr>
<tr>
<td>Simplify the exponents.</td>
<td><img alt="5 times 4 minus 8 times negative 2 plus 4." src="https://data.ulearngo.com/assets/a7eb3847-bd6b-434a-91c1-338c10bf1459"/></td>
</tr>
<tr>
<td>Multiply.</td>
<td><img alt="20 plus 16 plus 4." src="https://data.ulearngo.com/assets/10012de3-4bd4-419c-b97c-04745ddeb38f"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="40." src="https://data.ulearngo.com/assets/cd6768ba-795b-46bc-965b-957da2566b81"/></td>
</tr>
</tbody>
</table>
<table summary="This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says “Substitute 0 for x.” The right column contains 5 times 0 squared minus 8 times 0 plus 4. One row down, the left column says “Simplify the exponents.” The right column contains 5 times 0 minus 8 times 0 plus 4. One row down, the left column says “Multiply.” The right column contains 0 plus 0 plus 4. One row down, the left column says “Simplify.” The right column contains 4.">
<tbody>
<tr>
<td>$x=0$</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="5 x squared minus 8 x plus 4." src="https://data.ulearngo.com/assets/b272ae97-0437-46f7-ae26-17431b0fab02"/></td>
</tr>
<tr>
<td><img alt="Substitute 0 for x." src="https://data.ulearngo.com/assets/3a2e6da0-187d-4ec7-9ccd-1f68d0bae367"/></td>
<td><img alt="5 times 0 squared minus 8 times 0 plus 4." src="https://data.ulearngo.com/assets/8ea5dd17-b126-4081-a7ee-ffd00f94611b"/></td>
</tr>
<tr>
<td>Simplify the exponents.</td>
<td><img alt="5 times 0 minus 8 times 0 plus 4." src="https://data.ulearngo.com/assets/75f18f40-b6b6-48be-9ed7-5a84eced008d"/></td>
</tr>
<tr>
<td>Multiply.</td>
<td><img alt="0 plus 0 plus 4." src="https://data.ulearngo.com/assets/e5a19ca9-6147-463a-b501-c51a4d6434b6"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="4." src="https://data.ulearngo.com/assets/88e52187-6c89-4902-ae89-0946318d79ea"/></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>The polynomial $-16{t}^{2}+250$ gives the height of a ball $t$ seconds after it is dropped from a 250 foot tall building. Find the height after $t=2$ seconds.</p>
</div>
<div>
<h3>Solution</h3>
<p>$\begin{array}{cccc}&amp; &amp; &amp; \phantom{\rule{4em}{0ex}}-16{t}^{2}+250\hfill \\ \text{Substitute}\phantom{\rule{0.2em}{0ex}}t=2.\hfill &amp; &amp; &amp; \phantom{\rule{4em}{0ex}}-16{\left(2\right)}^{2}+250\hfill \\ \text{Simplify.}\hfill &amp; &amp; &amp; \phantom{\rule{4em}{0ex}}-16·4+250\hfill \\ \text{Simplify.}\hfill &amp; &amp; &amp; \phantom{\rule{4em}{0ex}}-64+250\hfill \\ \text{Simplify.}\hfill &amp; &amp; &amp; \phantom{\rule{4em}{0ex}}186\hfill \\ &amp; &amp; &amp; \phantom{\rule{4em}{0ex}}\text{After 2 seconds the height of the ball is 186 feet.}\hfill \end{array}$</p>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>The polynomial $6{x}^{2}+15xy$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side <em>x</em> feet and sides of height <em>y</em> feet. Find the cost of producing a box with $x=4$ feet and $y=6$ feet.</p>
</div>
<div>
<h3>Solution</h3>
<table summary="This figure has two columns. At the top of the figure, the right column contains 6x squared plus 15xy. One row down, the left column says “Substitute x equals 4, y equals 6”. The right column contains 6 times 4 squared plus 15 times 4 times 6. One row down, the left column says “Simplify.” The right column contains 6 times 16 plus 15 times 4 times 6. One row down, the left column says “Simplify.” The right column contains 96 plus 360. One row down, the left column says “Simplify.” The right column contains 456">
<tbody>
<tr>
<td> </td>
<td><img alt="6 x squared plus 15 x y." src="https://data.ulearngo.com/assets/d3583b94-c943-4c62-85f2-60dcb0450fc9"/></td>
</tr>
<tr>
<td><img alt="Substitute x equals 4 and y equals 6." src="https://data.ulearngo.com/assets/6ead9d0e-1641-4d52-8787-cb94c88f87b4"/></td>
<td><img alt="6 times 4 squared plus 15 times 4 times 6." src="https://data.ulearngo.com/assets/d59de35e-6ba9-4133-99c5-e652a4852354"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="6 times 16 plus 15 times 4 times 6." src="https://data.ulearngo.com/assets/e87f8f77-d094-4333-89e6-05ea922079b5"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="96 plus 360." src="https://data.ulearngo.com/assets/00998836-77af-4a89-80d1-b0a45cde2b85"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="456." src="https://data.ulearngo.com/assets/e72e8214-50fe-4308-bbce-4f69ab500ad9"/></td>
</tr>
<tr>
<td> </td>
<td>The cost of producing the box is $456.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>

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Evaluating a Polynomial For a Given Value

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Discover how to identify, evaluate, add, subtract, multiply, and divide various types of polynomials, and simplify expressions using exponents and scientific notations in this tutorial.


Evaluating a Polynomial For a Given Value

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