Graphing Polynomial Worksheet
Sketch the graph of each function.
1. f(x) = (x + 1)(x – 2)(x – 4)
2. f(x) = -(x + 3)(x + 2)(x – 1)3
3. f(x) = -x(x + 5)2(x + 3)
4. f(x) = x5 - 3x4 - x3 + 3x2
5. f(x) = -x5 + 4x4 - 4x3
6. f(x) = x2(x - 1)2(2 + x)
Write the equation for each polynomial graph shown below.
7.
8.
Equation
Equation
9. Sketch the graph of the equation with a double root at –2, a single root at 5, a triple root at 0
and a double root at 2. Assume the leading coefficient is negative. Write the equation of the
function that describes the graph.
Equation: ________________________________
10. Sketch the graph of the equation y = -x3 + 2x2 - x
Write the equation of the polynomial using the given information and then sketch the graph of
the polynomial.
11.
Zeros: -4, 0, 5, 7
Degree: 5
Graph touches x-axis at x = 5
Contains the point (4, 192)
Equation
12. Zeros: -1, 2
Degree: 4
Graph touches x-axis at x = -1 and x = 2
Contains the point (3, -48)
Equation
Graphing Polynomial Worksheet – Answer Key
Sketch the graph of each function.
1. f(x) = (x + 1)(x – 2)(x – 4)
-1
2
4
2. f(x) = -(x + 3)(x + 2)(x – 1)3
-3
-2
1
3. f(x) = -x(x + 5)2(x + 3)
-5
-3
4. f(x) = x5 - 3x4 - x3 + 3x2
y = x2(x - 3)(x - 1)(x +1)
-1
1
3
5. f(x) = -x5 + 4x4 - 4x3
y = -x3(x - 2)2
2
6. f(x) = x2(x - 1)2(2 + x)
-2
7.
y = (x + 4)(x + 1)2(x - 2)(x - 4)
8.
y = -(x + 6)2(x + 3)3(x - 1)(x - 4)2(x - 7)2
9.
y= -x3(x + 2)2(x - 2)2(x – 5)
1
10.
11.
y= -x(x - 1)2
f(x) = 2x(x + 4)(x – 5)2(x – 7)
12. f(x) = -3(x + 1)2(x -2)2