15. Q15a
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Similar Question 1
<p>Draw a graph of a polynomial function that satisfies all of the following characteristics:</p> <ul> <li><code class='latex inline'>f(-3) = 16, f(3) = 0, \text{ and } f(-1) = 0</code></li> <li>The y-intercept is 2.</li> <li><code class='latex inline'>f(x) \geq 0</code> when <code class='latex inline'>x < 3</code></li> <li><code class='latex inline'>f(x) \leq 0</code> when <code class='latex inline'>x > 3</code></li> <li>The domain is the set of real numbers.</li> </ul>
Similar Question 2
<p>Sketch a graph of a cubic polynomial function <code class='latex inline'>y = f(x)</code> such that <code class='latex inline'>f(x) < 0</code> when <code class='latex inline'>-4 < x < 3</code> or <code class='latex inline'>x > 7</code> and <code class='latex inline'>f(x) >0</code> when <code class='latex inline'>x < -4</code> or <code class='latex inline'>3 < x < 7</code>.</p>
Similar Question 3
<p>The solutions below correspond to inequalities involving a cubic function. For each solution, write two possible cubic polynomial inequalities, one with the less than symbol <code class='latex inline'>(<)</code> and the other with the greater than symbol <code class='latex inline'>(>)</code>.</p><p><code class='latex inline'>-\frac{2}{3} < x < \frac{4}{5}</code> <strong>or</strong> <code class='latex inline'>x > 3.5</code></p>
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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>Determine an expression for <code class='latex inline'>f(x)</code> in which <code class='latex inline'>f(x)</code> is a quartic function, <code class='latex inline'>f(x) > 0</code> when <code class='latex inline'>-2 < x < 1</code>, <code class='latex inline'>f(x) \leq 0</code> when <code class='latex inline'>x < -2</code> or <code class='latex inline'>x > 1</code>, <code class='latex inline'>f(x)</code> has a double root when <code class='latex inline'>x = 3</code>, and <code class='latex inline'>f(-1) = 96</code>.</p>
<p>Sketch a graph of a cubic polynomial function <code class='latex inline'>y = f(x)</code> such that <code class='latex inline'>f(x) < 0</code> when <code class='latex inline'>-4 < x < 3</code> or <code class='latex inline'>x > 7</code> and <code class='latex inline'>f(x) >0</code> when <code class='latex inline'>x < -4</code> or <code class='latex inline'>3 < x < 7</code>.</p>
<p>Write two possible quartic inequalities, one using the less than or equal to symbol and the other using the greater than or equal symbol, that correspond to the following solution:</p> <ul> <li><code class='latex inline'>-6 - \sqrt{2} < x < -6 + \sqrt{2}</code> or </li> <li><code class='latex inline'>6 - \sqrt{2} < x < 6 + \sqrt{2}</code></li> </ul>
<p>Draw a graph of a polynomial function that satisfies all of the following characteristics:</p> <ul> <li><code class='latex inline'>f(-3) = 16, f(3) = 0, \text{ and } f(-1) = 0</code></li> <li>The y-intercept is 2.</li> <li><code class='latex inline'>f(x) \geq 0</code> when <code class='latex inline'>x < 3</code></li> <li><code class='latex inline'>f(x) \leq 0</code> when <code class='latex inline'>x > 3</code></li> <li>The domain is the set of real numbers.</li> </ul>
<p>Describe what the solution to each inequality indicates about the graph of <code class='latex inline'>y=f(x)</code>.</p><p><code class='latex inline'>f(x) < 0</code> when <code class='latex inline'>-2 < x < 1</code> or <code class='latex inline'>x > 6</code></p>
<p>The solutions below correspond to inequalities involving a cubic function. For each solution, write two possible cubic polynomial inequalities, one with the less than symbol <code class='latex inline'>(<)</code> and the other with the greater than symbol <code class='latex inline'>(>)</code>.</p><p><code class='latex inline'>x < -1 - \sqrt{3}</code> <strong>or</strong> <code class='latex inline'>-1 + \sqrt{3} < x < 4</code></p>
<p>The solutions below correspond to inequalities involving a cubic function. For each solution, write two possible cubic polynomial inequalities, one with the less than symbol <code class='latex inline'>(<)</code> and the other with the greater than symbol <code class='latex inline'>(>)</code>.</p><p><code class='latex inline'>-\frac{2}{3} < x < \frac{4}{5}</code> <strong>or</strong> <code class='latex inline'>x > 3.5</code></p>
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