Factors, Roots, Zeros For a Polynomial Function: The Factors are:(x + 5) and (x - 3) The Zeros are -5 and 3 The x-intercepts are at: -5 or 3 The Roots/Solutions.

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Presentation transcript:

Factors, Roots, Zeros For a Polynomial Function: The Factors are:(x + 5) and (x - 3) The Zeros are -5 and 3 The x-intercepts are at: -5 or 3 The Roots/Solutions to x 2 + 2x -15 = 0 are: x = -5 and 3 Math 30-11

3.4 Multiplicity least possible degree zeros and their multiplicity The number of times a zero of a polynomial function occurs with multiplicity of 1 0 with multiplicity of 1 1 with multiplicity of 1 2 with multiplicity of 1 minimum at y = -6.9 when x =-1.3 least possible degree zeros and their multiplicity 4 -1 with multiplicity of 2 1 with multiplicity of 1 2 with multiplicity of 1 minimum at y = -1.6 when x = 1.6 Math 30-12

least possible degree zeros and their multiplicity 4 -1 with multiplicity of 1 1 with multiplicity of 1 2 with multiplicity of 2 minimum at y = -4.9 when x =-0.4 least possible degree zeros and their multiplicity 4 -2 with multiplicity of 2 1 with multiplicity of 2 minimum at y = 0 when x = -2 or 1 leading coefficient is positive Math 30-13

least possible degree zeros and their multiplicity 5 -1 with multiplicity of 3 1 with multiplicity of 1 2 with multiplicity of 1 no minimum or maximum least possible degree zeros and their multiplicity 5 -1 with multiplicity of 2 1 with multiplicity of 1 2 with multiplicity of 2 no minimum or maximum leading coefficient is positive Math 30-14

The graph of a polynomial y = f(x) is shown. What is the minimum possible degree for the polynomial function? Determine an equation of the function in factored form. Degree 4 zeros of the function are at-3, 1, and 5(multiplicity of 2) How could we determine the value of a? y-int at (0, 5) Math 30-15

y-int at (0, 5) Math 30-16

Analyzing Equations to Sketch Graphs of Polynomial Functions 3.4 McGrawHill Smart Notebook Math 30-17

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Sketching Graphs of Polynomial Functions Using Transformations Basic Graphs Transformations Math

Describe the transformations in words. Determine the coordinates of the image for each given point. vertical reflection about the x-axis y → -y The graph of the function y = x 3 is transformed to obtain the graph of. y = -(½(x - 5)) 3 -4 horizontal stretch about the y-axis by factor of 2 x → 1/2x horizontal translation 5 units right 1/2x → 1/2(x - 5) vertical translation 4 units down -y → -(y + 4) (x, y)→ (-2,-8)→ (-1, -1)→ (0, 0)→ (1, 1)→ (2, 8)→ ( 2x+5, -y-4 ) ( 1, 4 ) ( 3, -3 ) ( 5, -4 ) ( 7, -5) ( 9, -12 ) Math

Math The graph of the function y = 2(x-1) 4 is transformed to obtain the graph of. y = -((x + 2)) Describe the transformations in words. vertical reflection about the x-axis vertical stretch about the x-axis by a factor of ½ horizontal translation 3 units left vertical translation 1 unit up Graphing Polynomial Functions Page 147: 1a,c, 2c, 3b,c, 4a,c,d, 5, 6, 7a, 9a,c,e, 10a,c, 11 Solving Problems Page , 13, 14, 15, 16