25. Q25b
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Similar Question 1
<p>Given</p><p><code class='latex inline'> \displaystyle f(x) = \begin{cases} ax^2+bx + c, &(-\infty, 2] \\ (2-x)^3 +10x, &(2, \infty] \end{cases} </code></p><p>If <code class='latex inline'>f(x)</code> is continuous at <code class='latex inline'>x = 2</code>, at <code class='latex inline'>x = -1</code> the tangent is horizontal, and the y-intercept is 4, then find <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code>.</p>
Similar Question 2
<p>Given</p><p><code class='latex inline'> \displaystyle f(x) = \begin{cases} ax^2+bx + c, &(-\infty, 2] \\ (2-x)^3 +10x, &(2, \infty] \end{cases} </code></p><p>If <code class='latex inline'>f(x)</code> is continuous at <code class='latex inline'>x = 2</code>, at <code class='latex inline'>x = -1</code> the tangent is horizontal, and the y-intercept is 4, then find <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code>.</p>
Similar Question 3
<p>Given</p><p><code class='latex inline'> \displaystyle f(x) = \begin{cases} ax^2+bx + c, &(-\infty, 2] \\ (2-x)^3 +10x, &(2, \infty] \end{cases} </code></p><p>If <code class='latex inline'>f(x)</code> is continuous at <code class='latex inline'>x = 2</code>, at <code class='latex inline'>x = -1</code> the tangent is horizontal, and the y-intercept is 4, then find <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</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>Given</p><p><code class='latex inline'> \displaystyle f(x) = \begin{cases} ax^2+bx + c, &(-\infty, 2] \\ (2-x)^3 +10x, &(2, \infty] \end{cases} </code></p><p>If <code class='latex inline'>f(x)</code> is continuous at <code class='latex inline'>x = 2</code>, at <code class='latex inline'>x = -1</code> the tangent is horizontal, and the y-intercept is 4, then find <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code>.</p>
<p>Write a possible equation for a function that satisfies all of below. Explain your choice.</p> <ul> <li><code class='latex inline'>\displaystyle \lim_{x\to 5^+}f(x) = -\infty</code> and <code class='latex inline'>\displaystyle \lim_{x\to 5^-}f(x) = \infty</code></li> <li><code class='latex inline'>\displaystyle \lim_{x\to \infty}f(x) =2</code> and <code class='latex inline'>\displaystyle \lim_{x\to -\infty}f(x) = 2</code></li> <li><code class='latex inline'>\displaystyle f(4) = 3</code> and <code class='latex inline'>\displaystyle f(6) = 1</code></li> </ul>
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