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Warm Up Add or Subtract the following polynomials: 1.(2x 2 4y + 7xy 6y 2 ) (-3x 2 + 5y 4xy + y 2 ) 2.If P = 4x 4 - 3x 3 + x 2 - 5x + 11 and Q = -3x 4 + 6x 3 - 8x 2 + 4x - 3, what is P + Q?

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Recall from Math 2 Can anyone remember what the zeros of a function are? Where the graph touches the x-axis The x intercepts Where y = 0

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The zero of a function is just the value at which a function touches the x-axis. Note: This can be where it crosses or touches

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It is easy to find the roots of a polynomial when it is in factored form! (x - 3) and (x + 5) are factors of the polynomial. Factored Polynomial

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(x - 3) and (x + 5) are factors of the polynomial. (x - 3)(x + 5) = 0 (we want to know where the polynomial crosses the x-axis so we want to know what values of x will output 0) So (x 3) = 0 and (x + 5) = 0 The zeros are x = 3, x = -5 NOTE: It is NOT always the opposite! What if (2x 3) was a factor?

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Warm Up: Find the roots of the following factored polynomials. 1.y = (x-2) 3 (x+3)(x-4) 2.y = (x-5)(x+2) 3 (x-14) 2 3.y = (x+3)(x-15) 4 4.y = x 2 (x+6)(x-6)

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Sometimes the polynomial wont be factored! Ex.

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2nd TRACE (CALC) 2: zero

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Choose a point to the left of the zero. Then press ENTER. This arrow indicates that youve chosen a point to the left of the zero.

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Choose a point to the rightof the zero. Then press ENTER. This arrow indicates that youve chosen a point to the right of the zero.

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Press ENTER one more time!

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Find the zeros of the following polynomials:

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Solutions

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End Behavior The end behavior of a graph describes how the graph looks to the far left and the far right. How would you describe the end behavior of this graph?

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End Behavior We can determine the end behaviors of a polynomial using the leading coefficient and the degree of a polynomial. Leading coefficient Degree

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First determine whether the degree of the polynomial is even or odd. Next determine whether the leading coefficient is positive or negative. degree = 2 so it is even Leading coefficient = 2 so it is positive

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Degree EvenOdd Leading Coefficient ++ HighHighLowHigh LowLowHighLow

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Find the end behavior of the following polynomials.

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Classwork and Homework Complete the worksheet Left Side: Class work Right side: Homework