Preview to 6.7: Graphs of Polynomial

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Presentation transcript:

Preview to 6.7: Graphs of Polynomial

Finishing 6.7: Graphing Polynomials How do we find x and y –intercepts?

Check It Out! Example 3a Graph the function. f(x) = x3 – 2x2 – 5x + 6. Step 1 Identify the possible rational roots by using the Rational Root Theorem. p = 6, and q = 1. ±1, ±2, ±3, ±6 Step 2 Test all possible rational zeros until a zero is identified. Test x = –1. Test x = 1. –1 1 –2 –5 6 1 1 –2 –5 6 –1 3 2 1 –1 –6 1 –3 –2 8 1 –1 –6 x = 1 is a zero, and f(x) = (x – 1)(x2 – x – 6).

Check It Out! Example 3a Continued Step 3 Write the equation in factored form. Factor: f(x) = (x – 1)(x + 2)(x – 3) The zeros are 1, –2, and 3. Step 4 Plot other points as guidelines. y-intercept f(–1) = 8, and f(2) = –4.

Check It Out! Example 3a Continued Step 5 Identify end behavior. The degree is odd and the leading coefficient is positive so as x –∞, P(x) –∞, and as x +∞, P(x) +∞. Step 6 Sketch the graph of f(x) = x3 – 2x2 – 5x + 6 by using all of the information about f(x). In your textbook 6.7 complete questions 10, 11, 23, 24, 25, 26 **Check answers in the back of the book!!