Vertex & Vertex Form
Standard Form
Transformations
Key Features
Applications (Word Problems)
100
What is the vertex of
f(x)=3(x-4)^2-1
(4,-1)
100
What is the y-intercept of
f(x)=4x^2+5x-9
(0,-9)
100
Does this parabola shift left or right 6 units?
f(x)=1/2(x+6)^2-4
Left
100
What is the y-intercept of the graph?
What is
(0,7)
100
What key feature of a parabola represents the maximum height of an object?
The vertex
200
What is the vertex of the graph?
What is
(3,1)
200
What is the formula to find the "h" value of the vertex (also the axis of symmetry).
(-b)/(2a)
200
True or false. This parabola reflects downward AND compresses by 2.
f(x)=-2(x+1)^2-3
False
200
What is the axis of symmetry of the parabola:
f(x)=-1/3(x+4)^2-1
x=-4
200
A rocket is launched in the air and reaches a maximum height before falling to the ground. The equation that models the path of the rocket is below. What is the y-intercept of this model?
f(x)=-5x^2+30x+10
(0,10)
300
Given a function that has transformed from the parent function by reflecting, stretching by 3, shifting left 5, and down 6, what is the vertex of the new parabola?
(-5,-6)
300
What is the axis of symmetry in the parabola:
x=-3
300
Describe the transformations of the quadratic
f(x)=1/3(x-2)^2
compress by 1/3, shift right 2.
300
What are the x-intercepts of the graph
None
300
The path of a football thrown in the air is modeled by the function below, how long does it take (in seconds) to reach its maximum height?
f(x)=-16x^2+72x+4
2.25 seconds
400
Write a function in vertex form that includes the following transformations: Right 7, up 4, reflects, and stretches by 2.
f(x)=-2(x-7)^2+4
400
Given the quadratic in vertex form, convert it to standard form.
f(x)=3(x-2)^2-4
f(x)=3x^2-12x+8
400
Write the vertex form of a parabola that transforms by: shifting up 3, reflects, compresses by 1/2, and shifts left 2.
f(x)=-1/2(x+2)^2+3
400
Where is the graph positive? Write the interval.
(0,4)
400
The path of a football thrown in the air is modeled by the function below, what is the maximum height of the football?
f(x)=-16x^2+72x+4
85
500
Write the vertex form of a parabola with the vertex at
(-5,3) and a point (-6,-5)
f(x)=-2(x+5)^2-3
500
Given standard form, find the x-intercepts.
f(x)=x^2+12x+32
(-8,0) and (-4,0)
500
If a parabola has been transformed by reflecting, shifting right 3, and down 2, then write the standard form of this transformed function.
f(x)=-x^2+6x-11
500
Write the decreasing interval for the graph:
500
If the graph models the path of a rocket, what is a reasonable estimate for the height that the rocket was launched from?
80 feet