NC.M3.U2.F-BF.1a Re-Test Lesson

NC Math 3 Unit 2
Re-Test Lesson

Standard: F-BF.1a

Instructions:
Earn an 80% or higher on this lesson to be able to re-attempt the questions that you missed tied to this standard from our Unit 2 Test.

The Zeros and Factors of a Function are related

The degree of the function matches the number of zeros that the function has.

Some zeros may be "nonreal" which means that they will not be visible on the x-axis.

The function below has 6 zeros because it is of degree 6.

Multiple Select

A polynomial function contains the factors x, x-3, and x+1. Which graphs could represent the polynomial function. SELECT ALL THAT APPLY

Multiple Choice

If the function $$p\left(x\right)$$ has a zero at 5, which of the following is a true statement?

• (x-5) is a factor of p(x)

• (x+5) is a factor of p(x)

• p(x) has a

  y-intercept at (0,5)

• p(x) has 3 real solutions

Multiple Choice

Which of the polynomials below *could* have at most 6 zeros?

• $$f\left(x\right)=4x^4-5x^2-14$$

• $$f\left(x\right)=-2x^6+4x^4-3x^2+2x-9$$

• $$f\left(x\right)=3x^5-4x^3+2x-9$$

Fill in the Blank

At most, how many zeros does the polynomial below have?

$$f\left(x\right)=5x^4-7x^2+1$$  

X-intercepts

Write an equation for the graph by writing the x-intercepts as factors

Multiple Choice

Which equation matches the graph?

• 
  

  $$y=\left(x+1\right)\left(x+2\right)$$
  

• $$y=\left(x+1\right)\left(x-2\right)$$

• $$y=x\left(x+2\right)$$

• $$y=\left(x+2\right)\left(x-1\right)$$

• $$y=x^2+3x+2$$

Multiple Choice

Which equation matches the graph?

• $$y=\left(x-3\right)\left(x+2\right)\left(x-1\right)$$

• $$y=\left(x-3\right)\left(x-2\right)\left(x-1\right)$$

• $$y=\left(x+3\right)\left(x-2\right)\left(x+1\right)$$

• $$y=x\left(x-1\right)\left(x+2\right)\left(x+3\right)$$

Math Response

Write the equation for the polynomial function that is graphed.

Type your answer as "y=" instead of "f(x)=".

Type answer here

Correct Answer: y=4\left(x-1\right)\left(x+1\right)\left(x+2\right)

Deg^°

Rad

Math Response

Write the equation for the polynomial function that is graphed.

Type your answer as "y=" instead of "f(x)=".

Type answer here

Correct Answer: y=\frac{1}{4}\left(x+1\right)^2\left(x+6\right)

Deg^°

Rad