Show:
A. O. S.
Vertex
Roots
Discriminant
Characteristics
100
A.O.S.: y = x^2 - 26
What is x = 0
100
Vertex: y = x^2 – 6
What is (0, -6)
100
Roots: y = x^2
What is x = 0
100
Discriminant: y = x^2 – 2
What is d = 8 (2 Solutions)
100
Characteristics: The equation for: a = 1; b = -5; c = 4
What is y = x^2 - 5x + 4
200
A.O.S.: y = -x^2 + 4x - 3
What is x = 2
200
Vertex: y = -x^2 + 4x - 3
What is (2, 1)
200
Roots: y = x^2 + 6x + 9
What is x = {-3}
200
Discriminant: y = -x^2 + 4x – 3
What is d = 4 (2 Solutions)
200
Characteristics: This must be true if the parabola opens upwards.
What is a is positive
300
A.O.S.: y = -x^2 - 14x - 3
What is x = -7
300
Vertex: y = -x^2 - 14x – 3
What is (-7, 46)
300
Roots: y = -4x^2 - 24x
What is x = {-6, 0}
300
Discriminant: y = -2x^2 - 7x - 7
What is d = -7 (0 Solutions)
300
Characteristics: This divides the parabola into two symmetrical parts.
What is the axis of symmetry?
400
A.O.S.: y = x^2 - 10x + 16
What is x = 5
400
Vertex: y = x^2 - 10x + 16
What is (5, -9)
400
Roots: y = x^2 - 10x + 16
What is x = {2, 8}
400
Discriminant: y = x^2 + 16
What is d = - 64 (0 Solutions)
400
Characteristics: This is the domain for all quadratic equations
What is negative infinity to infinity
500
A.O.S.: y = -4x^2 - 24x
What is x = -3
500
Vertex: y = -4x^2 - 24x
What is (-3, 36)
500
Roots: y = -x^2 - x - 3
What is No Solution
500
Discriminant: y = 9x^2 - 6x + 1
What is d = 0 (1 Solution)
500
Characteristics: This is the range when the vertex (3, -7) is a maximum
What is y = negative infinity to -7 or y <= -7