2 x (x+3) 2 In these cases, we can take advantage of graphing utilities. ) To improve this estimate, we could use advanced features of our technology, if available, or simply change our window to zoom in on our graph to produce Figure 24. Hi, How do I describe an end behavior of an equation like this? (x+1) x n 202w and f Step 3. ) We have already explored the local behavior of quadratics, a special case of polynomials. 4. x h(x)= ) 6 ( Try It \(\PageIndex{17}\): Construct a formula for a polynomial given a graph. There are no sharp turns or corners in the graph. ]. The graph curves down from left to right touching the origin before curving back up. \end{align*}\], \( \begin{array}{ccccc} ( 3 axis. x (0,4). x has Starting from the left side of the graph, we see that -5 is a zero so (x + 5) is a factor of the polynomial. We say that \(x=h\) is a zero of multiplicity \(p\). 4 , x=1, Keep in mind that some values make graphing difficult by hand. The maximum number of turning points is A local maximum or local minimum at Lets first look at a few polynomials of varying degree to establish a pattern. x=3 n x Squares The polynomial is given in factored form. If the value of the coefficient of the term with the greatest degree is positive then that means that the end behavior to on both sides. In this section we will explore the local behavior of polynomials in general. 4 We can always check that our answers are reasonable by using a graphing calculator to graph the polynomial as shown in Figure 5. The sign of the lead. Find the y- and x-intercepts of 2, m( by factoring. ) x=0.01 2 x 2 9 2 The graph curves up from left to right passing through the origin before curving up again. h(x)= x=5, New blog post from our CEO Prashanth: Community is the future of AI . V= a This book uses the Since the graph is flat around this zero, the multiplicity is likely 3 (rather than 1). f(a)f(x) 0
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