Describing Terms
End Behavior
Intercepts
Vertex Form
Application
100
Find the degree of the term:
-18
0
( Imagine: -18x0)
100
f(x) = -x2
As x -> ∞
f(x) -> ___
-∞
100
What are the x-intercepts?
f(x) = (x+2)(x-4)(x+1)
(-2,0)
(4,0)
(-1,0)
100
What is the location of the vertex:
f(x) = (x - 2)2 + 4(2,4)
100
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h(t) = −16t2 + 84t + 72 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
Interpret h(4) = 152
At 4 seconds, the ball is 152 feet above the ground.
200
Find the degree of the term:
-4x7
7
200
f(x) = x7
As x -> -∞
f(x) -> ___
-∞
200
Find the y-intercept (in this case, "f intercept"):
f(x) = (x-5)(x+4)(x-2)
(0,40)
200
Find the location of the vertex:
h(n) = 4(n + 5)2 + 7
(-5, 7)
200
The height y (in feet) of a ball thrown by a child is
y = -1/12x^2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
Interpret y(2) = 6.67
At a horizontal distance away from the ball's starting point of 2 feet, the ball is 6.67 feet above the ground.
300
Find the degree of the polynomial:
−7 − 12x6 + 5x4 − 3x8
8
300
f(n) = −2n6 − 3n5 + 4n3 − 3
As n -> ∞
f(n) -> ___
-∞
300
What are the n-intercepts?
g(n) = (n-7)(n+4)(n+9)
(7,0)
(-4,0)
(-9,0)
300
Name the vertical stretch/compression:
g(x) = 3(x - 4)2 + 5
Vertical STRETCH of 3
(from vertex: over 1, up 3)
400
What is the leading coefficient of:
−2x5 − 5 − 4x4 + 4x6
4
400
f(n) = -4n4 - 3n5 - 2n3 + 8
As n -> -∞
f(n) -> ___
∞
400
Find the n-intercepts:
C(t) = 3n4 - 30n3 + 63n2
(0,0)
(3,0)
(7,0)
400
Find the vertex and vertical stretch/compression:
k(b) = 5(b - 9) - 3
Vertex: (9, -3)
Vertical STRETCH of 5
400
The height y (in feet) of a ball thrown by a child is
y = -1/12x^2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
How high is the ball immediately when it leaves the child's hand?
h(0) = 3
"At a horizontal distance of 0 feet, the ball is 3 feet above the ground"
500
What is the maximum number of real zeros:
−x2 − 5 + 4x4 − 3x3
4
500
f(x) = 8x7- 2x4 + 5x9 + 7
As x -> -∞
f(x) -> ___
-∞
500
Find the "f(r)-intercept:"
f(r) = -r3 + 14
(0,14)
500
Name a point on the graph that is not the vertex. (Hint: use vertex and vertical stretch)
h(t) = 2(t - 2)2 + 4
(3, 6)
500
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h(t) = −16t2 + 84t + 72 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
How many seconds does it take until the ball hits the ground?
h(6) = 0
"At 6 seconds, the ball is 0 feet off the ground"