1. Lesson 7.2 Finding Critical Features of Quadratic Equations
Objective - To algebraically find critical features of parabolic curves.
Quadratic Equation
Quadratic
Term
Linear
Term
Constant
Term a c
opens up
y-intercept +a -a
opens down
shifts up +c
skinny parabola
shifts down -c
wide parabola
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. Finding Critical Features of Quadratics
Graph
Axis
x=3 x y
y has no
maximum x y -3 -2 -1 1 2 3 29 18 10
x has no
mimimum
x has no
maximum 2 -3 -6
Vertex
Minimum Value
(3,-7) -7
y = -7 4 5 -6 -3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. Finding Critical Features of Quadratics
Vertex
Axis of Symmetry
Opens Up/Down
Opens Up
Y-intercept
(0, 2)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. Find the critical features of the quadratic below.
Vertex
Axis of Symmetry
Opens Up/Down
Opens Down
Y-intercept
(0, 0)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. Find the critical features of the quadratic below.
Vertex
Axis of Symmetry
Opens Up/Down
Opens Up
Y-intercept
(0, 4)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. and then find the critical features of the quadratic algebraically.
Graph x y x y -3 -2 -1 1 2 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. and then find the critical features of the quadratic algebraically.
Graph x y
Axis
Vertex
(1,9)
Vertex
x = 1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. and then find the critical features of the quadratic algebraically.
Graph
Y-int.= 8
y-intercept
Vertex x y
(1,9)
Opens Up/ Down?
Max. or Min Value
x = 1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series