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The Vertex and Intercepts of a Function

9.10.1 The Vertex and Intercepts of a Function

9.10.1 • The Vertex and Intercepts of a Function

Warm Up

These expressions each define the same function.

  • x 2 + 6 x + 8 x 2 + 6 x + 8
  • ( x + 2 ) ( x + 4 ) ( x + 2 ) ( x + 4 )
  • ( x + 3 ) 2 − 1 ( x + 3 ) 2 − 1

Without graphing or doing any calculations, determine where the following features would be on a graph that represents the function.

1.

What is the x x -coordinate of the vertex (of the graph)?

The x x -coordinate of the vertex (of a graph).

The x x -coordinate of the vertex is -3.

2.

What is the y y -coordinate of the vertex (of the graph)?

The y y -coordinate of the vertex (of a graph).

The y y -coordinate of the vertex is -1.

3.

Select both x x -intercepts .

  1. ( − 2 , 0 ) ( − 2 , 0 )
  2. ( − 6 , 0 ) ( − 6 , 0 )
  3. ( − 4 , 0 ) ( − 4 , 0 )
  4. ( − 8 , 0 ) ( − 8 , 0 )

The x x -intercepts are ( − 2 , 0 ) ( − 2 , 0 ) and ( − 4 , 0 ) ( − 4 , 0 ) .

4.

What is the y y -coordinate of the y y -intercept?

The y y -coordinate of the y y -intercept ( 0 , _ _ _ _ _ ) ( 0 , _ _ _ _ _ )

8. The y y -intercept is ( 0 , 8 ) ( 0 , 8 ) .