9.1 Exploring Quadratic Graphs
Objective: SWBAT
graph quadratic
functions and find roots
or x-intercepts.
Mini Quiz 22
2.
Overview
Quadratic functions y = ax2 + bx + c (no b for
today)
 Identifying maximum and minimum
 Comparing widths of parabolas
 Graphing the parabola
 Finding the vertex
Quadratic Function
Standard Form:
y  ax  bx  c, where a  0
2
What is a, b, and c for the following quadratic
Parabola: U-shaped graph for
functions?
quadratic function
Leading
2 + 3x – 4
1.
y
=
2x
Coefficient
2. y = x2 – x + 9
3. y = -x2 – 7
Vertexhighest or
lowest point
on the
parabola
Parabola – Quadratic Functions
Important
“Points”
x-intercepts,
roots, zeros
Does the
graph have a
maximum or a
minimum?
vertex (on the axis
of symmetry x = #)
Vertex, Axis of Symmetry, and
Max or Min
1.
Vertex (0, 0); x = 0; Min
2.
Vertex (-2, 4); x = -2; Max
3.
Vertex (4, 3); x = 4; Max
4.
Vertex (1, -2); x= 1; Min
Identify the vertex and axis of symmetry. Tell whether it is a minimum or maximum.
Who’s the widest of them all?
1 2
Widest: y  x ; y  x2 ;y  4x2
4
The “smaller” the “a” is, the wider the graph
Graphing the Parabola
Steps:
1. Make a T-chart
2. Find the vertex:
(axis of
b
x
symmetry)
2a
3. Graph 2 points to each
side of the vertex
4. Draw the parabola
5. Write the x-intercepts
x = -2, x = 0
Graph: y = x2 + 2x
x
y
1
0
3
0
-1
-1
-2
0
-3
3
Graph and Write the x-intercepts
1. y  2 x
1 2
2. y  x
2
2
3. y  x  3
2
x=0
x=0
x = No
Solution
1 2
4. y   x  2 x = -2
2
x=2
Wrap Up
Quadratic functions y = ax2 + bx + c (no b for today)
 Identifying maximum and minimum
 Comparing widths of parabolas
 Graphing the parabola
b
x
– Find vertex:
2a
– Pick 2 points on each side of the vertex
– Graph the parabola
HW: P. 429 #1-29 EOO
DLUQ: What is the formula for the axis of symmetry
and the vertex for the x-coordinate?