Understanding Quadratic Functions
The shape of the graph. (mathematical term)
What is a parabola?
Vertex form of a Quadratic Function
What is y=a(x-h)^2+k
Is this a Quadratic Function: f(x)=x+1
Explain WHY!
No, it is a linear function because there is no
x^2 term
The point through which the parabola turns direction.
What is the vertex?
Vertex
What is (h,k)
Is this a quadratic function? f(x)= x^2+2x-6
Explain WHY!
Yes because it has an
x^2
A vertical line that passes through the vertex and divides the parabola into two symmetrical halves.
What is axis of symmetry?
Graph opens upward or downward f(x)=-5(x-1)^2+2
downward
Describe the transformation of the vertex:
(x+4)^2-8
4 to the left and 8 down
Identify the axis of symmetry f(x)=(x+3)^2 -4
x=-3
State the Vertex of the quadratic
f(x)=-2(x-3)^2+1
What is (3,1)
Describe the transformation of the vertex:
f(x)=(x-1)^2-13
1 to the right and 13 down
How can you determine whether a function is quadratic or not by looking at its graph?
If the graph is a parabola or not
State the domain and range of f(x)=(x-2)^2-4
domain: R / Range y greater than -4
Describe the transformation of f(x)= 0.5(x-1)^2 + 6
1 unit to the right, vertical compression by factor 0.5 and 6 units up