3. Q3d
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Similar Question 1
<p> Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.</p><img src="/qimages/9867" />
Similar Question 2
<p>Which equation models the data in the table? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { F } y=x^{2}-1 & \text { (H) } y=-x^{2}+3 \\ \text { (G) } y=x^{2}+3 & \text { D } y=x^{2}+1\end{array} </code></p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline x & y \\ \hline 1 & 4 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 19 \\ \hline\end{array} </code></p>
Similar Question 3
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{cc}x & y \\ 0 & -4 \\ 2 & 2 \\ 4 & 8 \\ 6 & 14 \\ 8 & 20\end{array} </code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/5537" />
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/601" />
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/602" />
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1497" /><p><code class='latex inline'>\displaystyle \begin{array}{|l|r|r|r|r|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{y} & 4 & 7 & 12 & 17 \\ \hline \end{array} </code></p>
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/600" />
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{rr}x & y \\ \hline-2 & 2 \\ -1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 2\end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{|r|r|}\hline x & y \\ \hline 0 & -2 \\ \hline 1 & -2 \\ \hline 2 & 0 \\ \hline 3 & 4 \\ \hline 4 & 10 \\ \hline\end{array} </code></p>
<p>Determine the standard equation of the polynomial function represented by the table of values.</p><img src="/qimages/3860" />
<p> Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|r|r|r|r|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{y} & -1 & 4 & 15 & 32 & 55 \\ \hline \end{array} </code></p>
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1499" /><p><code class='latex inline'>\displaystyle \begin{array}{|l|r|r|r|r|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{y} & 1 & -1 & 7 & -11 \\ \hline \end{array} </code></p>
<p>The first three diagrams in a pattern are shown. Each square has a side length of 1 unit.</p><img src="/qimages/762" /> <ul> <li></li> </ul>
<p>State whether each relation is quadratic. Justify your answer.</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \boldsymbol{y} & 3 & 2 & 1 & 0 & 1 & 2 \\ \hline \end{array} </code></p>
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/5536" />
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{rr}\mid x & y \\ \hline 0 & 1 \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \\ 4 & 16\end{array} </code></p>
<p> Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|r|r|r|r|} \hline \boldsymbol{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{y} & 0 & -5 & 0 & 15 & 40 \\ \hline \end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{|r|r|}\hline x & y \\ \hline 1 & -10 \\ \hline 3 & 0 \\ \hline 5 & 18 \\ \hline 7 & 44 \\ \hline 9 & 78 \\ \hline\end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{rr}\boldsymbol{x} & \boldsymbol{y} \\ -2 & 10 \\ -1 & 6 \\ 0 & 2 \\ 1 & -2 \\ 2 & -6\end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{rr}\boldsymbol{x} & \boldsymbol{y} \\ 0 & 0 \\ 1 & 1 \\ 2 & 8 \\ 3 & 27 \\ 4 & 64\end{array} </code></p>
<p>The first three diagrams in a pattern are shown. Each square has a side length of <code class='latex inline'>1</code> unit.</p><img src="/qimages/762" /> <ul> <li></li> </ul>
<p>Which equation models the data in the table? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { F } y=x^{2}-1 & \text { (H) } y=-x^{2}+3 \\ \text { (G) } y=x^{2}+3 & \text { D } y=x^{2}+1\end{array} </code></p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline x & y \\ \hline 1 & 4 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 19 \\ \hline\end{array} </code></p>
<p>Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|r|r|r|r|} \hline \boldsymbol{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{y} & 0 & -5 & 0 & 15 & 40 \\ \hline \end{array} </code></p>
<p> Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|r|r|r|r|} \hline \boldsymbol{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{y} & -3 & 3 & 5 & 3 & -3 \\ \hline \end{array} </code></p>
<p>A ball is dropped from a distance <code class='latex inline'>\displaystyle 10 \mathrm{~m} </code> above the ground. The height of the ball from the ground is measured every tenth of a second, resulting in the following data:</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|c|l|l|l|l|l|l|l|l|} \hline Time (s) & 0.0 & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 \\ \hline Height (\mathbf{m}) & 10.00 & 9.84 & 9.36 & 8.56 & 7.44 & 6.00 & 4.24 & 2.16 & 0.00 \\ \hline \end{array} </code></p><p>a) Use difference tables to determine whether distance, <code class='latex inline'>\displaystyle d(t) </code>, is a linear or quadratic function of time. Explain.</p><p>b) What are the domain and range of this function? Express your answer in set notation.</p>
<p>Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|r|r|r|r|r|} \hline \boldsymbol{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{y} & -3 & 3 & 5 & 3 & -3 \\ \hline \end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline x & y \\ \hline 0 & 3 \\ \hline 1 & 5 \\ \hline 2 & 7 \\ \hline 3 & 9 \\ \hline 4 & 11 \\ \hline\end{array} </code></p>
<p>The table shows the length of a spring under a specific load.</p><img src="/qimages/6189" /><p><strong>a)</strong> Use finite differences to determine whether this is a quadratic relation.</p><p><strong>b)</strong> Make a scatter plot of the data. Draw a curve of best fit.</p><p><strong>c)</strong> Use your curve of best fit to predict the length of the spring under a load of <code class='latex inline'>8</code> kg</p>
<p>Use finite differences to determine whether each function is linear, quadratic, or neither.</p><p><code class='latex inline'>\displaystyle \begin{array}{rr}\boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -1 \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7\end{array} </code></p>
<p> Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.</p><img src="/qimages/9868" />
<p> Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.</p><img src="/qimages/9867" />
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{cc}x & y \\ 0 & -4 \\ 2 & 2 \\ 4 & 8 \\ 6 & 14 \\ 8 & 20\end{array} </code></p>
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1501" /><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y & 1 & 2 & 4 & 8 & 16 \\ \hline \end{array} </code></p>
<p> Use finite differences to determine whether each function is linear, quadratic, or neither.</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline x & y \\ \hline 0 & 3 \\ \hline 1 & 4 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 19 \\ \hline\end{array} </code></p>
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1496" /><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|} \hline \boldsymbol{x} & 10 & 20 & 30 & 40 \\ \hline \boldsymbol{y} & 21 & 41 & 61 & 81 \\ \hline \end{array} </code></p>
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1498" /><p><code class='latex inline'>\displaystyle \begin{array}{|l|r|r|r|r|} \hline \boldsymbol{x} & 5 & 6 & 7 & 8 \\ \hline \boldsymbol{y} & -2 & -3 & -5 & -8 \\ \hline \end{array} </code></p>
<ol> <li>Use finite differences to determine whether each function is linear, quadratic, or neither.</li> </ol> <p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline x & y \\ \hline 0 & 0 \\ \hline 1 & 2 \\ \hline 2 & 6 \\ \hline 3 & 12 \\ \hline 4 & 20 \\ \hline\end{array} </code></p>
<p>Using <code class='latex inline'>y = 0.6(x - 3)(x + 2)</code> when <code class='latex inline'>x=3.2</code>.</p><img src="/qimages/2489" />
<p>Use finite differences to determine whether each relation is linear, quadratic, or neither.</p><img src="/qimages/5535" />
<p>Calculate the first differences for each set of data, and determine whether the relation is linear or nonlinear. If the relation is nonlinear, determine the second differences and identify the quadratic relations.</p><img src="/qimages/1500" /><p><code class='latex inline'>\displaystyle \begin{array}{|l|r|r|r|r|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{y} & -2 & -1 & 6 & 25 \\ \hline \end{array} </code></p>
<p>The path of a rocket fired at a Canada Day fireworks display is given by <code class='latex inline'>h = -4.9t^2 + 19.6t + 0.4</code>, where h is the height, in metres, of the rocket above the ground and t is the time, in seconds.</p><p>(a) Make a table of values for t = 0 to t = 4.</p><p>(b) Make a table of first and second differences. What conclusion can you make?</p><p>(c) Draw a graph of the path of the rocket using the table of values from part a) or graphing technology. Describe the path of the rocket.</p><p>(d ) How high above the ground was the rocket when it was set off? Explain your answer.</p>
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