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Sketching the graph of a polynomial function
1.
2. Solve for x and y intercepts
Solving for the x and y intercepts is an important role step in
graphing a polynomial function. These intercepts are used to
determine the points the graphs intercepts or touches the x-axis
and the y-axis.
To find the x-intercept of a polynomial function:
a. Factor the polynomial completely
b. Let y be equal to zero
c. Equate each factor to zero and solve for x
To find the y-intercept:
a. Let x be equal to zero and simplify
3. End of Behavior x4 – 5x2 + 4
Condition 1:
An > 0
n is an odd number
Q1 and Q3
Condition 3:
An < 0
n is an odd number
Q2 and Q4
Condition 2:
An > 0
n is an even number
Q1 and Q2
Condition 4:
An < 0
n is an even number
Q3 and Q4
4. No. of turning points
The number of turning points is at most (n – 1)
Multiplicity of roots
If r is a zero of odd multiplicity, the graph of P(x)
crosses the x – axis at r.
If r is a zero of even multiplicity, the graph of P(x) is
tangent to the x axis at r.
5. Since the roots are 1, -1, 2, and -2 the x-intercepts are (1, 0), (-1,
0), (2, 0), (-2,0).
Make a table of values and assign values of x between these
roots and also values of x higher than the bigger root (2) and
lower than smaller root(-2). Then solve.
x -2 -1 0 1 2 3 -3 0.5 -0.5 1.5 -1.5
y 0 0 4 0 0 40 40 2.81 2.81 -2.19 -2.19
6. Solve for y-intercept:
y = x4 – 5x2 + 4
y = (0)4 – 5(0)2 + 4
y = 0 – 5(0) + 4
y = 0 – 0 + 4
y = 0
So, the y intercept is (0,4).