02.08 Polynomial

02.08 Polynomial

Multiple Choice

The table below is graphed on Desmos.

Which of the following curve/line BEST fit the points graphed from the table?

Did you get it right?

Now the equation for this curve is:

 $y=-0.01x^3+0.43x^2-3.30x+10.08$  Use this equation to predict the value of y when x is 12. You'll type the answer on the next slide.

Fill in the Blanks

What is the y-value you got from the previous slide?

Finding Zeros (and Graphing) - see Packet on the last sheet

• If it's in factored form (x-a)(x-b)(x-c), then solve the zeros by "taking the opposite"

• Plot the zeros on the x-axis

• For y-intercept, plug in 0 to x and calculate

Multiple Select

Check Understanding: 

Select the correct set of zeros AND the correct y-intercept for the following polynomial function:  $f\left(x\right)=\left(x+7\right)\left(x+2\right)\left(x-2\right)$  

• Zeros: x = 7, 2, and -2

• Zeros: x = -7, -2, and 2

• Zeros x = -7 and -2 only

• y-int: (0, -28)

• y-int: (0, 28)

Multiple Select

Check Understanding 2: 

Select the correct set of zeros AND the correct y-intercept for the following polynomial function:  $f\left(x\right)=3x\left(x+1\right)\left(x-5\right)$  

• Zeros: x = 0, -1, and 5

• Zeros: x =  -1 and 5

• Zeros x = -3, -1, and 5

• y-int: (0, 0)

• y-int: (0, 15)

Multiplicity of Zeros (work on the packet; last sheet)

• The exponent associated with each factor (x-a) is the multiplicity

• If the multiplicity is ODD (1, 3, 5, 7, ...), the curve/line will CROSS the x-axis on that zero/x-int

• If the multiplicity is EVEN (2, 4, 6, 8, ...), the curve/line will only TOUCH/BOUNCE on the x-axis at that zero/x-int

• The degree of the polynomial is the sum of the multiplicities of all the zeros

Multiple Choice

Check understanding:

Click on the image. Which of the following can be the equation for this polynomial graph?

•  $f\left(x\right)=x^3\left(x+2\right)^2$  

•  $f\left(x\right)=x^2\left(x+2\right)^2$  

•  $f\left(x\right)=x^3\left(x+2\right)^3$  

•  $f\left(x\right)=x^2\left(x+2\right)^3$  

Last Thing(s)!

• Complete Desmos Activity drawing

• Complete Khan Academy (1)