Standard Form
Opens up, because the coefficient on x2 is positive.
Which directions does the h value in Vertex form move the graph?
y=a(x-h)2+k
Left and Right. +h is right and -h is right
What is easy to find when a quadratic is in intercept form?
y=a(x-p)(x-q)
x-intercepts
Does the following graph have a max or min?
Max
The shape that is made by the quadratic function when graphed.
What is the y-intercept for the quadratic function?
y=3x2-x+3
(0,3)
Which Direction does the k value move the graph in the vertex form?
y=a(x-h)2+k
The k value shifts the graph up and down. +k up and -k down.
What are the x-intercepts for the quadratic function
y= (x-2)(x+4)
(2,0) and (-4,0)
What is the vertex of the graph?
(3,2)
The highest or lowest point on a quadratic graph? Also referred to as the "turning point"
Vertex
What is the formula for axis of symmetry?
y=2x2-4x+2
x=1
What is the vertex for the parabola give by
y=2(x-3)2-2?
(3,-2)
What are the x-intercepts for the quadratic function
y=x(x+1)
(0,0) and (-1,0)
What is the range of the Quadratic Function?
y< 3
The quadratic graph is divided in half by this imaginary line.
Axis of Symmetry
What is the axis of symmetry for the quadratic function?
y=-x2+6x-3
x= 3
Which way does the graph for y=-(x+2)2+1 open?
Opens up.
What is the axis of symmetry for the quadratic function?
y=(x-2)(x-4)
x=3
What are the x-intercepts of the quadratic graph?
(-1,0) and (3,0)
Where a graph crosses the x-axis
X-intercept
What is the vertex for the quadratic function?
y=2x2+4x-5
(-1,-7)
Write a quadratic in vertex form that has the following transformations.
-Shifted up 2
-Shifted left 1
- More narrow
2(x+1)2+2
y=(x-1)(x+3)
(0,-3)
When is the graph increasing and decresing?
Increasing: (-inf,2)
Decreasing: (2,inf)
The point where a graph crosses the y-axis
y-intercept