Lesson 9-B Notes – Algebra 1

Graphing Quadratic Functionsfrom Vertex Form

TNSS F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
TNSS F-IF. 4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
TNSS F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (Graph linear and quadratic functions and show intercepts, maxima, and minima.)

Past Target
I graphed linear functions. / Present Target
I can graph quadratic functions. / Future Target
I will solve quadratic equations by graphing.

REVIEW: Identify the Axis of Symmetry, the Vertex, and whether it’s a maximum or a minimum.

A. Axis of Symmetry: B. Axis of Symmetry: C. Axis of Symmetry:

Vertex: Vertex: Vertex:

Max / Min: Max / Min: Max / Min:

Vertex Form of a quadratic function:

Vertex :

Standard Form:  Same Quadratic Function  Vertex Form:

Axis of Sym.: Vertex:

Vertex: Axis of Sym:

Ex. 1 – Identify the vertex and axis of symmetry for each of the following quadratic functions.

A. Vertex : ( , ) Axis of Symmetry: x =

B. Vertex : ( , ) Axis of Symmetry: x =

C. Vertex : ( , ) Axis of Symmetry: x =

D. Vertex : ( , ) Axis of Symmetry: x =

YOU TRY:

E. Vertex : ( , ) Axis of Symmetry: x =

F. Vertex : ( , ) Axis of Symmetry: x =

G. (Hint: x is x-?) Vertex : ( , ) Axis of Symmetry: x =

H. Vertex : ( , ) Axis of Symmetry: x =

Part A: Determine whether the parabola opens up or down.

Part B: Find the coordinates of the vertex.

Part C: Write the equation of the axis of symmetry.

Part D: Identify the vertex as a maximum or minimum.

Part E: Graph the function. (see steps 1-6 on the 8-A notes)

Part F: State the domain and the range of the function.

Practice with Graphing Quadratics from Vertex Form

1.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

2.

  1. Direction of opening is ______
    Happy  or Sad 
  1. Vertex ______
  2. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

3.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

4.

  1. a.Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

5.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

6.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

7.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range:

8.

  1. Direction of opening is ______
    Happy  or Sad 
  2. Vertex ______
  1. Axis of Symmetry ______
  1. The vertex is a ______point

(max. or min.)

  1. Make a table:
  1. Domain:

Range: