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Lesson: Recognizing Features of Quadratic Functions

In this lesson, we will learn how to identify features of quadratic equations, such as its vertex, maximum or minimum value, axis of symmetry, domain, and range.

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01:33

Worksheet • 22 Questions • 1 Video

Q1:

Find the coordinates of the vertex of the graph of 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 6 π‘₯ βˆ’ 4 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

  • A The vertex is ( 3 , βˆ’ 1 3 ) , the value of the function at the vertex is βˆ’ 1 3 , it is a minimum value.
  • B The vertex is ( 3 , βˆ’ 1 3 ) , the value of the function at the vertex is βˆ’ 1 3 , it is a maximum value.
  • C The vertex is ( 3 , βˆ’ 1 3 ) , the value of the function at the vertex is 3, it is a minimum value.
  • D The vertex is ( βˆ’ 1 3 , 3 ) , the value of the function at the vertex is 3, it is a maximum value.
  • E The vertex is ( βˆ’ 1 3 , 3 ) , the value of the function at the vertex is βˆ’ 1 3 , it is a minimum value.

Q2:

Find the coordinates of the vertex of the graph of 𝑓 ( π‘₯ ) = π‘₯ + 4 π‘₯ + 5 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

  • A The vertex is ( βˆ’ 2 , 1 ) , the value of the function at the vertex is 1, it is a minimum value.
  • B The vertex is ( βˆ’ 2 , 1 ) , the value of the function at the vertex is 1, it is a maximum value.
  • C The vertex is ( βˆ’ 2 , 1 ) , the value of the function at the vertex is βˆ’ 2 , it is a minimum value.
  • D The vertex is ( 1 , βˆ’ 2 ) , the value of the function at the vertex is βˆ’ 2 , it is a maximum value.
  • E The vertex is ( 1 , βˆ’ 2 ) , the value of the function at the vertex is 1, it is a minimum value.

Q3:

Find the coordinates of the vertex of the graph of 𝑓 ( π‘₯ ) = βˆ’ π‘₯ + 2 π‘₯ + 2 2 . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

  • A The vertex is ( 1 , 3 ) , the value of the function at the vertex is 3, it is a maximum value.
  • B The vertex is ( 1 , 3 ) , the value of the function at the vertex is 3, it is a minimum value.
  • C The vertex is ( 1 , 3 ) , the value of the function at the vertex is 1, it is a maximum value.
  • D The vertex is ( 3 , 1 ) , the value of the function at the vertex is 1, it is a minimum value.
  • E The vertex is ( 3 , 1 ) , the value of the function at the vertex is 3, it is a maximum value.
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