Graphing Quadratics
Identify the Vertex, the Axis of Symmetry, and the minimum/maximum value of f(x) = (x + 5)2 + 2.
Vertex: (-5, 2)
Axis of Symmetry: x = -5
Minimum Value: 2
Factor the following: x2 + 3x + 2
(x + 1) (x + 2)
Solve the equation: 2x2 + 16 = 30
x = sqrt(7), -sqrt(7)
Simplify the following: sqrt (8)
2sqrt(2)
On a math test, 5 out of 20 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the test?
60/6840 -> 1/114
Identify the Vertex, the Axis of Symmetry, and the minimum/maximum value of f(x) = -x2 + 2x - 3.
Vertex: (1, -2)
Axis of Symmetry: x = 1
Maximum value: -2
Factor the following: 2x2 - x - 15
(2x + 5) (x - 3)
Use the Quadratic Formula to solve the equation: x2 - 5x + 3 = 0
x = (5 - sqrt(13)) / 2, (5 + sqrt(13)) / 2
Simplify the following: sqrt (-48)
4isqrt(3)
A car's distance from it's starting position (in meters) can be modeled by d(t) = 6t + 8 where t represents time (in seconds). Calculate the car's speed (rate of change) between 2 and 7 seconds.
6 m/sec
Identify the Vertex, and the Domain and Range of f(x) = x2 - 2x - 3.
Domain: (-inf, inf)
Range: [-4, inf)
Factor the following: 6x2 + 11x + 4
(2x + 1) (3x + 4)
Solve the equation by Completing the Square: x2 + 16x + 62 = 0
x = -8 + sqrt(2), -8 - sqrt(2)
Simplify the following: 4i (3 - 2i)
8 + 12i
Use the information below to answer the question:
A B C D F
Male 5 7 4 2 3
Female 4 4 5 1 2
Find the probability of selecting a student with a B given the student is Female.
4/16 -> 1/4
Describe the transformation of the parent function of f(x) = 2(x - 4)2 + 1.
a = 2 -> stretch by a factor of 2
h = 4 -> horizontal shift right of 4 units
k = 1 -> vertical shift up of 1 unit
Factor the following and then find the solutions: f(x) = 2x2 + 13x + 15.
Factor: (x + 5) (2x + 3)
Solutions: x = -5, -3/2
Solve the equation by Completing the Square: y2 + 2y + 10 = 0
x = -1 - 3i, -1 + 3i
Simplify the following: (8 - 9i) (-6 + 9i)
33 + 126i
An object is dropped from top of a building. The object's distance from the ground (in feet) is modeled by d(t) = -16t2 + 375 where t represents time (in seconds). Calculate the object's rate of change between 2 and 5 seconds.
-112 ft/sec
Identify the Vertex, the Axis of Symmetry, and the Domain and Range of f(x) = -2x2 - 1. Then sketch the graph with the Axis of Symmetry.
Vertex: (0, -1)
Axis of Symmetry: x = 0
Domain: (-inf, inf)
Range: [-1, inf)
Factor the following and then find the solutions: f(x) = 9x2 - 27x + 20.
Factor: (3x - 5) (3x - 4)
Solutions: x = 5/3, 4/3
Use the Quadratic Formula to solve the equation: 2 = -4x2 - 5x
x = (-5 - i*sqrt(7))/8, (-5 + i*sqrt(7))/8
Simplify the following: 3 (4 - 2i) (2 + 2i) + (11 - 6i)
47 + 6i
The height of a flare fired from the deck of a ship in distress can be modeled by h(t) = -16t2 + 104t + 56 where h is the height of the flare above water and t is the time (in seconds). Calculate the flare's rate of change between 1 and 3 seconds.
40 ft/sec