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
Solve this equation:
x2-25=0
(5,0) and (-5,0)
Simplify and classify this function
2x^2 - 3x + 4 - x^2 + 6x + 4
x^2 + 3x + 8
Quadratic Trinomial
The point through which the parabola turns direction.
What is the vertex?
In the general vertex form, what is the 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
Solve the following equation:
49x2-16 = 0
(4/7,0) and (-4/7,0)
Name the type of function represented by the function:
y-6=2x^2
Quadratic Function
A vertical line that passes through the vertex and divides the parabola into two symmetrical halves.
What is axis of symmetry?
What does "k" do in vertex form?
Vertical Shift
Describe the transformation of the vertex:
-2(x+4)^2-8
4 to the left and 8 down
solve this equation:
x2 - 23 = 0
y= (sqrt(23),0) and (-sqrt(23),0)
Write the Quadratic function in standard form
3+y+5x^2=6x
y=-5x^2+6x-3
What part of a parabola can the vertex be?
minimum or maximum
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)=5(x-1)^2-13
1 to the right and 13 left
Solve this equation:
9x2 - 24 = 0
((2sqrt(6))/3,0) and ((-2sqrt(6))/3,0)
Find the axis of symmetry of the function:
y= (x-2)^2 + 3
x = 2
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 vertex of the Quadratic Function
f(x) = (x+4)^2
What is (-4,0)
How can you determine whether a function is quadratic or not by looking at its graph?
What is the graph is a parabola.
solve this equation:
x2 + 9 = 0
(3i, 0) and (-3i, 0)
Write the quadratic function in vertex form
Vertical Stretch/Shrink: none
Horizontal Shift: right 2
Vertical shift: down 1
y=(x-2)^2-1