H Algebra 2/Trig · Unit 3
Sketch the graph. Label the x- and y-intercepts.
Sketch from the factors
Write each x-intercept and its multiplicity.
State the degree and whether the leading coefficient is positive or negative. Use the matching end behavior above.
The y-intercept is the value when x = 0. Label the x-intercepts and the y-intercept on the sketch.
Three intercepts, and the curve crosses at each one.
x = −2, Multiplicity 1
x = 1, Multiplicity 1
x = 4, Multiplicity 1
Degree 3, positive
y-intercept when x = 0
y = (0 + 2)(0 − 1)(0 − 4) = 8
Answer: y-intercept (0, 8)
x = −4, Multiplicity 1
x = −1, Multiplicity 1
x = 2, Multiplicity 1
Degree 3, positive
y-intercept when x = 0
y = (0 + 4)(0 + 1)(0 − 2) = −8
Answer: y-intercept (0, −8)
x = −3, Multiplicity 1
x = 2, Multiplicity 1
x = 5, Multiplicity 1
Degree 3, positive
y-intercept when x = 0
y = (0 + 3)(0 − 2)(0 − 5) = 30
Answer: y-intercept (0, 30)
x = −5, Multiplicity 1
x = −2, Multiplicity 1
x = 1, Multiplicity 1
Degree 3, negative
y-intercept when x = 0
y = −(0 + 5)(0 + 2)(0 − 1) = 10
Answer: y-intercept (0, 10)
x = −1, Multiplicity 1
x = 2, Multiplicity 1
x = 6, Multiplicity 1
Degree 3, positive
y-intercept when x = 0
y = (0 + 1)(0 − 2)(0 − 6) = 12
Answer: y-intercept (0, 12)
x = −3, Multiplicity 1
x = 1, Multiplicity 1
x = 4, Multiplicity 1
Degree 3, negative
y-intercept when x = 0
y = −(0 + 3)(0 − 1)(0 − 4) = −12
Answer: y-intercept (0, −12)
One intercept bounces.
x = −4, Multiplicity 2
x = 1, Multiplicity 1
x = 3, Multiplicity 1
Degree 4, positive
y-intercept when x = 0
y = (0 + 4)²(0 − 1)(0 − 3) = 48
Answer: y-intercept (0, 48)
x = −2, Multiplicity 1
x = 3, Multiplicity 2
x = 6, Multiplicity 1
Degree 4, positive
y-intercept when x = 0
y = (0 + 2)(0 − 3)²(0 − 6) = −108
Answer: y-intercept (0, −108)
x = −5, Multiplicity 2
x = −1, Multiplicity 1
x = 2, Multiplicity 1
Degree 4, negative
y-intercept when x = 0
y = −(0 + 5)²(0 + 1)(0 − 2) = 50
Answer: y-intercept (0, 50)
x = −3, Multiplicity 2
x = 2, Multiplicity 1
x = 4, Multiplicity 1
Degree 4, positive
y-intercept when x = 0
y = (0 + 3)²(0 − 2)(0 − 4) = 72
Answer: y-intercept (0, 72)
x = −1, Multiplicity 1
x = 2, Multiplicity 2
x = 5, Multiplicity 1
Degree 4, negative
y-intercept when x = 0
y = −(0 + 1)(0 − 2)²(0 − 5) = 20
Answer: y-intercept (0, 20)
x = −6, Multiplicity 2
x = −2, Multiplicity 1
x = 1, Multiplicity 1
Degree 4, positive
y-intercept when x = 0
y = (0 + 6)²(0 + 2)(0 − 1) = −72
Answer: y-intercept (0, −72)
Two bounces, or a fraction in front.
x = −4, Multiplicity 2
x = 1, Multiplicity 2
x = 6, Multiplicity 1
Degree 5, positive
y-intercept when x = 0
y = (18)(0 + 4)²(0 − 1)²(0 − 6) = −12
Answer: y-intercept (0, −12)
x = −5, Multiplicity 2
x = 2, Multiplicity 2
x = 4, Multiplicity 1
Degree 5, positive
y-intercept when x = 0
y = (14)(0 + 5)²(0 − 2)²(0 − 4) = −100
Answer: y-intercept (0, −100)
x = −3, Multiplicity 2
x = 1, Multiplicity 1
x = 5, Multiplicity 1
Degree 4, negative
y-intercept when x = 0
y = −(15)(0 + 3)²(0 − 1)(0 − 5) = −9
Answer: y-intercept (0, −9)
x = −2, Multiplicity 2
x = 3, Multiplicity 2
Degree 4, positive
y-intercept when x = 0
y = (16)(0 + 2)²(0 − 3)² = 6
Answer: y-intercept (0, 6)
x = −6, Multiplicity 2
x = −1, Multiplicity 2
x = 2, Multiplicity 1
Degree 5, negative
y-intercept when x = 0
y = −(18)(0 + 6)²(0 + 1)²(0 − 2) = 9
Answer: y-intercept (0, 9)
x = −3, Multiplicity 3
x = 2, Multiplicity 1
Degree 4, positive
y-intercept when x = 0
y = (0 + 3)³(0 − 2) = −54
Answer: y-intercept (0, −54)
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