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P. 396 #14

P. 396 #14. The Mathletes Lianne Ruiz Kianna Selkridge Samantha Silverstein. f(x)=(x-2)(x+4) 2. Step 1: Can this be factored any further? NO! The equation can not be factored any further because it is already in factored form. Factored Form: f(x)= (x-2)(x+4) 2.

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P. 396 #14

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  1. P. 396 #14 The Mathletes Lianne Ruiz KiannaSelkridge Samantha Silverstein

  2. f(x)=(x-2)(x+4)2 • Step 1: Can this be factored any further? • NO! • The equation can not be factored any further because it is already in factored form. • Factored Form: f(x)= (x-2)(x+4)2

  3. Finding the X intercepts… The x-intercepts are where the graph crosses the x-axis and a point where the y-value is zero. f(x)= (x-2)(x+4) 2 f(x) = (x-2 )(x+4) 2 X=2 ; x=-4 x-int(s):(2,0) and (-4,0)

  4. Finding the y intercepts… The y-intercepts are where the graph crosses the y-axis and a point where the x-value is zero. f(x)= (x-2)(x+4) 2 f(0) = (0-2 )(0+4) 2 -2 • 4 2 -2 • 16 = -32 y-int: (0,-32)

  5. Multiplicity • Step 1: Determine the multiplicity of the equation by checking it’s degree: F(x)=(x-2)(x+4)2 F(x)=(x-2)1(x+4)2 (x-2); (X+4)(X+4) X=2; x=-4and x=-4 So the multiplicity of x=2 is 1 and the multiplicity of x=-4 is 2.

  6. Touching and Crossing • Step1: Determine whether the graph will touch or cross by using the odd-even rule in Multiplicity. F(x)=(x-2)(x+4) 2 F(x)=(x-2)1(x+4)2 X=2; x=-4 x-int(s):(2,0) and (-4,0) X=2 has an odd multiplicity of 1, so at the point (2,0)the graph will cross. X=-4 has an even multiplicity of 2, so at the point (-4,0) the graph will touch.

  7. How do we find the graph of an equation? It is quite simple, the graph of an equation can be found by plotting points. Since we already have our x and y intercepts, we will not use those values on our chart. The following values were chosen as the value(s) of x.

  8. Finding the f(x) values… In order to find the f(x) value, the first step is to replace the X’s in the equation with each of the values listed in the chart below. (you may choose your own values)

  9. Finding the f(x) values… f(x)= (x-2)(x+4) 2 f(x)= (-5-2)(-5+4)2 f(x)= (1-2)(1+4)2 -7 •-12=-7 -1 • 25=-25 f(x)= (-3-2)(-3+4)2 f(x)= (2-2)(2+4)2 -5 • 1=-5 0 • 36= 0 f(x)= (-2-2)(-2+4)2 f(x)= (3-2)(3+4)2 -4 • 4=-16 1 • 49= 49

  10. Plotting the points on the graph…

  11. Hope this helps!The End! • ~Contributions: • Lianne Ruiz: Finding x and y intercepts • KiannaSelkridge: Factoring equation and crossing and touching • Samantha Silverstein: Finding and plotting F(x) point and Graph • PowerPoint was a done as a group.

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