Graphing Polynomials Worksheet
Grade 12 Math worksheet on graphing polynomial functions, including identifying key features and sketching graphs.
Includes
Standards
Topics
Graphing Polynomials
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Read each question carefully and provide complete answers. Show all your work for full credit. Sketch graphs neatly on the provided coordinate planes.
1. Consider the polynomial function P(x) = (x + 2)(x - 1)^2(x - 3).
a) Determine the degree of the polynomial.
b) List the x-intercepts and their multiplicities.
c) Describe the end behavior of the graph of P(x).
2. Sketch the graph of the polynomial function f(x) = -x^3 + 4x^2 - 4x.
a) Find the x-intercepts and y-intercept.
b) Determine the end behavior of the graph.
c) Create a sign chart for f(x).
d) Sketch the graph of f(x) on the coordinate plane below.
3. For a polynomial function of odd degree, the graph must cross the x-axis at least once.
True
False
4. Which of the following polynomial functions has a graph that rises to the left and falls to the right?
f(x) = x^3 - 2x + 1
f(x) = -2x^4 + x^2 - 5
f(x) = -x^5 + 3x^3 - x
f(x) = 3x^2 - 4x + 2
5. If a polynomial function has a root with an even multiplicity, its graph will the x-axis at that intercept.
6. The maximum number of turning points a polynomial of degree 'n' can have is .
7. A polynomial function has x-intercepts at -3 (multiplicity 1), 0 (multiplicity 2), and 2 (multiplicity 1). Its y-intercept is (0,0). The leading coefficient is positive. Sketch a possible graph of this function.