Maths Extension 1 Year 11 - Module 2 - Lesson 12
Graphing Polynomials
Name
Date
Class
1. Lesson focus
Graphing polynomial functions. Use real zeros and their multiplicities for x-intercepts, the leading term for end behaviour, and P(0) for the y-intercept.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. For the same cubic, state the y-intercept and end behaviour.
3. Describe how the graph meets the axis at each zero of P(x)=(x−3)³(x+1)².
3. Challenge
For Q(x)=−2(x−1)(x+2)², state the degree and end behaviour.
4. Multiple choice
The y-intercept of (x+2)(x−1)² is what?
A. 1
B. 0
C. −2
D. 2
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. For P(x)=(x+2)(x−1)², give its x-intercepts and multiplicities.
x=−2 has multiplicity 1; x=1 has multiplicity 2.
2. For the same cubic, state the y-intercept and end behaviour.
P(0)=2. Positive leading cubic: P→−∞ as x→−∞ and P→∞ as x→∞.
3. Describe how the graph meets the axis at each zero of P(x)=(x−3)³(x+1)².
It crosses with flattening at x=3 (odd multiplicity 3) and touches at x=−1 (even multiplicity 2).
Challenge. For Q(x)=−2(x−1)(x+2)², state the degree and end behaviour.
Degree 3, negative leading coefficient: Q→∞ as x→−∞ and Q→−∞ as x→∞.
Multiple choice. The y-intercept of (x+2)(x−1)² is what?
Correct answer: D. Substitute x=0: (2)(1)=2.
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