Understanding Quadratic Functions
The shape of the graph.
What is a parabola?
How is the parent function transformed:
g(x)=ax^2 with |a|>1
What is Vertical Compression.
What is vertex form of a quadratic equation?
f(x)= a(x-h)^2 + k
The point through which the parabola turns direction.
What is the vertex?
What is the axis of symmetry of the function y=-3(x-2)^2+1
x=2
Vertex of a Quadratic Function in standard form
What is (-b/2a , f(-b/2a))
What effect does "k" have on a quadratic function in standard form?
translates the function vertically
What is the vertex of the graph of the function f(x)= 2(x-2)^2-1
(4,-1)
Write f(x)= (x-1)^2 -4 in standard form
f(x)=x^2 -2x-3
Quadratic functions are polynomials of what degree?
2
f(x)=ax^2 opens downward and is wider than the parent function f(x)=x^2. What is a possible value for a?
a is a negative value between 0 and -1
What is the y-int of the graph of f(x)=(x-1)^2 - 4
-3 or (0, -3)
How do you find the Axis of symmetry of a quadratic function in standard form?
What is x= -b/2a
How can you determine if the function will have a maximum or minimum?
If a>0, the function will have a minimum
If a<0, the function will have a maximum
What function shows a parent function where the vertex has been translated right 3 and down 4?
f(x)= (x-3)^2 -4
How can you determine whether a function is quadratic or not by looking at its graph?
What is the graph is a parabola.
What is the axis of symmetry of the graph of the function f(x)= -x^2 - 6x + 8?
x= -3