Question

Randy is taking his math SAT. To receive full credit, he must answer this question:

What key features are necessary-and how are the features used-to create the sketch of a polynomial function?

What is Randy's correct answer, so he receives full credit for the question? Explain in complete sentences.

Answer 1

The key features of polynomials are the vertex, axis of symmetry, x and y intercepts. 1. The degree will help you find the end behavior.2. The vertex shows you where it changes concavity.3. X and y intercepts give you a couple of points of reference.4. Axis of symmetry is only applicable to even degree polynomials. I am hoping that these answers have satisfied your expectations, and if you would like, feel free to ask another question.

Answer 2

The key features are :

1. x-intercepts :

• Zeroes : To find zeroes set y=0 and solve for x and no. of zeroes are equal to degree of polynomial.

• Multiplicity : If the zero repeats even times then it touches the x-axis but if zero repeats odd times it will cross the x-axis.

2. y- intercepts :

• Set x=0 and Solve for y in order to find the y-intercepts of the graph of the polynomial function.

3. End Behavior :

• If the polynomial degree is odd, the end behavior goes in opposite directions.
• If the polynomial degree is even the end behavior goes in same direction.