Honors Algebra 2 Notes
Name________________
4.1 Graph Quadratic Functions in Standard Form
y = x2
Parent Function:
To Graph a Parabola:
Convert the function into vertex form:
(
y =a x !h
2
) +k
The y-coordinate of the vertex will be a
maximum or minimum value for the
parabola.
Use at least 5 points on the graph.
Vertex: ________
Axis of Symmetry: ________
Max / Min: ________
Graph the following parabolas on the same plane. Compare them to the Parent Graph.
1.
y = 2x 2
3.
y =
1
2
x 2 ! 2x + 3
2.
y = !
1
2
x2 + 3
Summary / Properties of Parabolas in Standard Form
y = ax 2 + bx + c
Graph opens up if
_____________
Graph opens down if
_____________
(Reflected over x-axis)
Graph is narrower if
_____________
Graph is wider if
(Vertically stretched)
_____________
(Vertically compressed)
Axis of Symmetry
_____________
y-intercept
_____________
Maximum Value if
_____________
Minimum Value if
_____________
EXAMPLE y = !2x 2 + 16x ! 31
a.
Describe the graph of y = !2x 2 + 16x ! 31
b.
Graph the parabola and compare it to your description.
c.
Investigate the Parabola. Always include these 8 parts.
Function in Vertex Form: ______________________________
Vertex
x-int
_______
_______
Max / Min
_______
y-int
_______
AOS
______
x-int
_______
Domain
_______
Range _____