Lesson Worksheet: Graphing Quadratic Functions Mathematics

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In this worksheet, we will practice graphing any quadratic function using a table of values and a given interval and identifying the features of the graph.

Q1:

Sketch the graph of the quadratic function 𝑓(𝑥)=𝑥−1 on the domain interval [−2,2] by completing the following table.

𝑥−2−1 0 1 2
𝑓(𝑥)⋯⋯⋯⋯⋯
  • A
  • B
  • C
  • D
  • E

Q2:

By completing the table of values for 𝑓(𝑥)=−𝑥+1, identify the correct graph of the quadratic function.

𝑥−2−1012
𝑓(𝑥)⋯⋯⋯⋯⋯
  • A
  • B
  • C
  • D
  • E

Q3:

Identify the 𝑥-intercepts of the quadratic function 𝑓(𝑥)=𝑥−1.

  • A𝑥=1, 𝑥=2
  • B𝑥=0, 𝑥=1
  • C𝑥=−1, 𝑥=1
  • D𝑥=−1, 𝑥=2
  • E𝑥=0, 𝑥=−1

Q4:

Identify the 𝑦-intercepts of the quadratic function 𝑓(𝑥)=𝑥−1.

  • A𝑦=−2
  • B𝑦=0
  • C𝑦=−1
  • D𝑦=1
  • E𝑦=2

Q5:

Identify the coordinates of the vertex of the quadratic function 𝑓(𝑥)=𝑥−1.

  • A(2,0)
  • B(0,0)
  • C(1,0)
  • D(−1,0)
  • E(0,−1)

Q6:

Identify the axis of symmetry of the quadratic function 𝑓(𝑥)=𝑥−1.

  • A𝑥=2
  • B𝑥=−2
  • C𝑥=−1
  • D𝑥=1
  • E𝑥=0

Q7:

By completing the table of values for 𝑓(𝑥)=(𝑥+2)−4, identify the correct graph of the quadratic function on the domain [−4,0].

𝑥−4−3−2−10
𝑓(𝑥)
  • A
  • B
  • C
  • D
  • E

Identify the 𝑥-intercepts of the given quadratic function.

  • A𝑥=−4, 𝑥=−2
  • B𝑥=2, 𝑥=−4
  • C𝑥=0, 𝑥=−2
  • D𝑥=4, 𝑥=0
  • E𝑥=−4, 𝑥=0

Identify the 𝑦-intercept of the given quadratic function.

  • A𝑦=−4
  • B𝑦=−2
  • C𝑦=4
  • D𝑦=2
  • E𝑦=0

Identify the axis of symmetry of the given quadratic function.

  • A𝑥=−4
  • B𝑥=2
  • C𝑥=−2
  • D𝑥=0
  • E𝑥=4

Identify the vertex of the given quadratic function.

  • A(−4,0)
  • B(4,0)
  • C(0,2)
  • D(−2,−4)
  • E(−4,−2)

Q8:

Which of the following graphs represents the quadratic function that has a vertex at (0,−1)?

  • A
  • B
  • C
  • D
  • E

Q9:

Consider the quadratic function 𝑓(𝑥)=𝑥−1.

Does the given quadratic function open upward or downward?

  • AUpward
  • BDownward

Does the given quadratic function have a maximum or a minimum value?

  • AMaximum
  • BMinimum

What is the maximum (or minimum) value of the given quadratic function?

  • A𝑦=0
  • B𝑦=2
  • C𝑦=−1
  • D𝑦=−2
  • E𝑦=1

Q10:

Which of the following graphs represents the quadratic function that intersects the 𝑥-axis at 𝑥=−1,𝑥=1 and the 𝑦-axis at 𝑦=−1?

  • A
  • B
  • C
  • D
  • E

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