Systems
Vertex Form
Standard Form
Key Features
Transformations
100
Solve the system graphically.
y = x2 + 2x - 8
y = 4x - 9
(1, -5)
100
The vertex of: y = (x+1)2 + 2
What is (-1,2) ?
100
The equation for finding the x value of the vertex from standard form
-b/2a
100
Algebraically,
(1) Is there a max or min?
(2) What is the y-intercept?
y = -x2 + 6x - 8
(1) Max
(2) (0, -8)
100
Describe all transformations related to the quadratic parent function.
k(x) = -3 (x+5)2 - 8
Left 5, Stretch 3, Reflect over x, Down 8
200
Solve the system graphically.
y = -x2 + 8
y = 2x + 5
(1,7) and (-3, -1)
200
The vertex of: y = (x+3)2
What is (-3, 0)
200
The leading coefficient being negative means
There is a reflection across the x-axis
200
Algebraically,
(1) What is the vertex?
(2) What is the axis of symmetry?
y = -x2 + 6x - 8
(1) (3,1)
(2) x = 3
200
What is the axis of symmetry?
y= 3x2 + 7
x = 0
300
Solve the system graphically.
y = 3
y = (x+1)2 + 3
(-1, 3)
300
Convert to vertex form: f(x) = x2 + 4x - 1
f(x) = (x + 2)2 - 5
300
The axis of symmetry: y= -x2 + 2x + 1
What is x = 1
300
Using interval notation,
(1) What is the domain?
(2) What is the range?
y = -x2 + 6x - 8
(1) (-∞, ∞)
(2) (-∞, 1]
300
Write a quadratic equation with the following transformations:
reflection over the x axis, compression by 1/5 units, shift right 3 units and shift upwards 8 units
y = - 1/5 (x-3)2 + 8
400
Solve the system algebraically.
y = x2 + 6x + 10
y = -2x - 6
(-4, 2)
400
Convert to vertex form f(x) = -2x2 + 8x - 8
f(x) = -2(x - 2)2
400
The vertex of: y = 3x2 - 12x +4
(2, -8)
400
List 5 coordinate points, including the vertex. Then graph.
y = -x2 + 6x - 8
(0,-8) (2,0) (3,1) (4,0) (6, -8)
400
Describe all transformations
y= 2x2 + 8x - 3
Left 2, stretch 2, down 11
500
Solve the system algebraically.
y + 6 = x2 - 2x
y - 10 = 4x
(8, 42) and (-2, 2)
500
Convert to vertex form:
f(x) = -2x2 + 4x - 9
f(x) = -2(x - 1)2 - 7
500
Algebraically,
(1) What is(are) the values of the x-intercept(s)?
(2) What is the value of the max/min?
y = -x2 + 6x - 8
(1) (2,0) (4,0)
(2) Max at 1
500
Using interval notation,
(1) What is the interval of increase?
(2) What is the interval of decrease?
y = -x2 + 6x - 8
(1) (-∞, 3)
(2) (3, ∞)
500
Write the quadratic equation for the given parabola.
y = -(x + 2)2 - 3