GRAPHING POLYNOMIAL FUNCTION by Richard Paulino.pptx

Graphing Polynomial Function

1. GRAPHING POLYNOMIAL FUNCTION RICHARD B. PAULINO MATH 10

2. Review: End Behavior of the Graph of a Polynomial Function 1. the degree of the polynomial is even and the leading coefficient is positive the graph is rising on both left and right 2. the degree of the polynomial is odd and the leading coefficient is positive the graph is falling at left and rising at the right. 3. the degree of the polynomial is even and the leading coefficient is negative the graph is falling on both left and right 4. the degree of the polynomial is odd and the leading coefficient is negative the graph is rising at left and falling at the right. Function Leading Coefficient Degree End Behavior of the Graph y=2x 3 -7x 2 -7x+12 y=-x 5 +3x 4 +x 3 -7x 2 +4 y=x 4 -7x 2 +6x y= -x 4 +2x 3 +13x 3 -14x+24 Y=(x+2) 2 (x-1) 4 (x+1) 3 (x-2) positive positive positive negative negative odd odd even even even Falling left and rising right Falling right and rising left Rising right and rising left Falling right and falling left Rising right and rising left

3. GRAPHING POLYNOMIAL FUNCTION I. Sketch the graph of the function y=(x-1)(x+2)(x-3)(x+4) STEPS: 1. Determine the x-intercept/s (roots/zeroes) of the graph. y=(x-1)(x+2)(x-3)(x+4) x-1=0 x+2=0 x-3=0 x+4=0 x=1 x=-2 x=3 x=-4 2. Determine the y-intercept of the graph. y=(x-1)(x+2)(x-3)(x+4) y=(-1)(+2)(-3)(+4) y=24 Arrange the roots in ascending order to determine the CRITICAL AREA. Roots : -4, -2, 1, 3

4. x=1 x=-2 x=3 x=-4 x-intercepts 24 -∞ ∞ 3. Determine the Critical Area. (-∞,-4) (-4,-2) (-2,1) (1,3) (3, ∞)

5. CRITICAL AREA (-∞,-4) (-4,-2) (-2,1) (1,3) (3, ∞) Factors/Test Value x-1 x+2 x-3 x+4 y=(x-1)(x+2)(x-3)(x+4) Position of the curve relative to the x-axis -5 -3 2 4 - - - + - - - - - + - - - - + + + + + + + + + + + above above above below below 4. Construct the table of signs

6. x=1 x=-2 x=3 x=-4 y=24 x-intercepts y-intercept 24 -∞ ∞ 5. Sketch the graph Number of turning points = Degree - 1 Number of turning points = 4 - 1 Number of turning points = 3

7. GRAPHING POLYNOMIAL FUNCTION I. Sketch the graph of the function y=(x+2) 3 (x-1) 2 STEPS: 1. Determine the x-intercept/s (roots/zeroes) of the graph. y=(x+2) 3 (x-1) 2 (x+2) 3 =0 (x-1) 2 =0 x=1 multiplicity 2 x=-2 multiplicity 3 2. Determine the y-intercept of the graph. y=(x+2) 3 (x-1) 2 y=(+2) 3 (-1) 2 y=(8)(1) y=8 Note: If the zero has an even multiplicity, then the graph is tangent to the x-axis. If the zero has an odd multiplicity, then the graph crosses the x-axis.

8. GRAPHING POLYNOMIAL FUNCTION I. Sketch the graph of the function y=(x+2) 3 (x-1) 2 STEPS: 3. Construct the table of signs x=-2 x=1 y=8 x-intercepts y-intercept CRITICAL AREA (-∞,-2) (-2,1) (1, ∞) Test Value -3 2 (x+2) 3 =0 - + + (x-1) 2 + + + y=(x+2) 3 (x-1) 2 - + + Position of the curve relative to the x-axis below above above

9. x=-2 x=1 y=8 x-intercepts y-intercept Note: If the zero has an even multiplicity, then the graph is tangent to the x-axis. If the zero has an odd multiplicity, then the graph crosses the x-axis.

10. Sketch the graph of for each function a. y=(x+1)(x-2)(x+4) b. y=(x-2) 2 (x+1) 3 c . y=-(x+1) 2 (x-1)(x-2) 2

11. GRAPHING POLYNOMIAL FUNCTION I. Sketch the graph of the function y=(x+2) 3 (x-1) 2 STEPS: 1. Determine the x-intercept/s (roots/zeroes) of the graph. y=(x+1)(x-2)(x+4) 2. Determine the y-intercept of the graph.c X+1=0 x-2=0 x+4=0 x=-1 x=2 x=4 Y-intercept =(1)(-2)(4)=-8