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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).

7. If x = 3
y = x4 – 5x2 + 4
= (3)4 – 5(3)2 + 4
= 81 – 5(9) + 4
= 81 – 45 + 4
= 36 + 4
= 40
If x = 0. 5
y = x4 – 5x2 + 4
= (0.5)4 – 5(0.5)2 + 4
= 0.0625 – 5(0.25) + 4
= 0.0625 – 1.25 + 4
= -1.1875 + 4
= 2.81
If x = -3
y = x4 – 5x2 + 4
= (-3)4 – 5(-3)2 + 4
= (81) – 5(9) + 4
= 81 – 45 + 4
= 40
If x = -0.5
y = x4 – 5x2 + 4
= (-0.5)4 – 5(0.5)2 + 4
= 0.0625 – 5(-0.25) + 4
= 0.0625 – 1.25 + 4
= 2.81

8. If x = 1.5
y = x4 – 5x2 + 4
= (1.5)4 – 5(1.5)2 + 4
= 5.0625 – 5(2.25) + 4
= 5.0625 – 11.25 + 4
= -6.1875 + 4
= -2.19
If x = -1.5
y = x4 – 5x2 + 4
= (-1.5)4 – 5(-1.5)2 + 4
= 5.0625 – 5(2.25) + 4
= 5.0625 – 11.25 + 4
= -6.1875 + 4
= -2.19
End of the behavior = Q1 and Q2
Leading term = x4
An > 0 ; (1 > 0)
n is an even number (4)
No. of turning points: (n – 1)
= (n – 1)
= 4 – 1
= 3

9. Sketch the graph