Worksheet: Graphing Quadratic Functions

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In this worksheet, we will practice graphing any quadratic function that is given in its standard and vertex forms using and studying its transformations.

Q1:

Which of the following graphs represents the equation 𝑦=π‘₯+3?

  • A
  • B
  • C
  • D
  • E

Q2:

What is the function whose graph is shown below?

  • A𝑓(π‘₯)=βˆ’(π‘₯+6)
  • B𝑓(π‘₯)=π‘₯+12π‘₯+72
  • C𝑓(π‘₯)=(π‘₯+6)
  • D𝑓(π‘₯)=(π‘₯βˆ’6)

Q3:

Which of the following graphs represents the equation 𝑦=βˆ’(π‘₯+3)(π‘₯βˆ’6)?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following graphs represents the equation 𝑦=(π‘₯+4)(π‘₯βˆ’2)?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following graphs represents the equation 𝑦=π‘₯(π‘₯βˆ’9)?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following graphs represents the equation 𝑦=π‘₯(3π‘₯+4)?

  • A
  • B
  • C
  • D
  • E

Q7:

Which of the following graphs represents the equation 𝑦=βˆ’5π‘₯βˆ’10π‘₯+6?

  • A
  • B
  • C
  • D
  • E

Q8:

The shown figure is a graph of a function 𝑓.

Which of the following functions has a larger maximum value than the function 𝑓?

  • A𝑔(π‘₯)=(π‘₯+1)(4βˆ’π‘₯)
  • B𝑔(π‘₯)=8βˆ’23(π‘₯βˆ’5)
  • C𝑔(π‘₯)=7π‘₯+4βˆ’2π‘₯
  • D𝑔(π‘₯)=7βˆ’|2+π‘₯|
  • E𝑔(π‘₯)=4π‘₯+7βˆ’2π‘₯

Q9:

The function drawn represents the quadratic 𝑓(π‘₯)=π‘š+π‘₯. Find the coordinates of 𝐡 and 𝐢 given 𝑂𝐴=4 units.

  • A𝐡=(0,βˆ’2), 𝐢=(0,2)
  • B𝐡=(0,2), 𝐢=(0,βˆ’2)
  • C𝐡=(βˆ’2,0), 𝐢=(2,0)
  • D𝐡=(2,0), 𝐢=(βˆ’2,0)

Q10:

Which of the following function types describes the graph shown?

  • AQuadratic
  • BAbsolute value
  • CReciprocal
  • DSquare root

Q11:

What function is represented in the figure below?

  • A𝑓(π‘₯)=π‘₯+8π‘₯+15
  • B𝑓(π‘₯)=π‘₯+15π‘₯+8
  • C𝑓(π‘₯)=π‘₯βˆ’15π‘₯+8
  • D𝑓(π‘₯)=π‘₯βˆ’8π‘₯+15
  • E𝑓(π‘₯)=βˆ’π‘₯βˆ’8π‘₯βˆ’15

Q12:

The curve drawn below represents the quadratic function 𝑓(π‘₯)=π‘₯βˆ’(π‘˜+1)π‘₯βˆ’π‘˜+3. Find the value of π‘˜ given 𝐴𝐡𝐢𝑂 is a square.

Q13:

The function drawn below represents the quadratic 𝑓(π‘₯)=βˆ’π‘₯+3π‘₯+π‘˜βˆ’2 which intersects the π‘₯-axis at the points 𝐴 and 𝐡. Find the value of π‘˜ given 𝑂𝐡=4𝑂𝐴.

Q14:

Write the quadratic equation represented by the graph shown. Give your answer in vertex form.

  • A𝑦=βˆ’(π‘₯+3)+4
  • B𝑦=(π‘₯βˆ’3)+4
  • C𝑦=βˆ’(π‘₯+3)βˆ’4
  • D𝑦=(π‘₯+3)βˆ’4
  • E𝑦=βˆ’(π‘₯βˆ’3)+4

Rewrite your equation in standard form.

  • A𝑦=π‘₯+6π‘₯+5
  • B𝑦=βˆ’π‘₯βˆ’6π‘₯βˆ’5
  • C𝑦=βˆ’π‘₯βˆ’6π‘₯βˆ’13
  • D𝑦=βˆ’π‘₯+6π‘₯βˆ’5
  • E𝑦=π‘₯βˆ’6π‘₯+13

Q15:

Which of the following is the equation of the function drawn on the graph?

  • A𝑦=3(π‘₯+4)+1
  • B𝑦=3(π‘₯+4)βˆ’1
  • C𝑦=3(π‘₯βˆ’4)βˆ’1
  • D𝑦=βˆ’3(π‘₯+4)βˆ’1
  • E𝑦=βˆ’3(π‘₯+4)+1

Q16:

Which of the following is the equation of the function drawn on the graph?

  • A𝑓(π‘₯)=π‘₯βˆ’8
  • B𝑓(π‘₯)=π‘₯+8
  • C𝑓(π‘₯)=βˆ’π‘₯βˆ’8
  • D𝑓(π‘₯)=π‘₯βˆ’8
  • E𝑓(π‘₯)=βˆ’π‘₯+8

Q17:

Which of the following graphs represents the equation 𝑦=βˆ’(π‘₯βˆ’4)+1?

  • A
  • B
  • C
  • D
  • E

Q18:

Which graph represents the function 𝑦=βˆ’0.5π‘₯+4?

  • A(a)
  • B(d)
  • C(c)
  • D(b)

Q19:

Write the quadratic equation represented by the graph shown. Give your answer in vertex form.

  • A𝑦=(π‘₯+2)(π‘₯+1)
  • B𝑦=(π‘₯βˆ’2)+1
  • C𝑦=(π‘₯βˆ’2)(π‘₯βˆ’1)
  • D𝑦=(π‘₯βˆ’1)βˆ’2
  • E𝑦=(π‘₯+2)βˆ’1

Rewrite your equation in standard form.

  • A𝑦=π‘₯βˆ’4π‘₯+5
  • B𝑦=π‘₯+3π‘₯+2
  • C𝑦=π‘₯βˆ’2π‘₯βˆ’1
  • D𝑦=π‘₯βˆ’3π‘₯+2
  • E𝑦=π‘₯+4π‘₯+3

Q20:

Which of the following graphs represents the equation 𝑦=2(π‘₯+3)βˆ’2?

  • A
  • B
  • C
  • D
  • E

Q21:

Which of the following graphs represents the equation 𝑦=(π‘₯βˆ’2)+5?

  • A
  • B
  • C
  • D
  • E

Q22:

Which of the following is the equation of the function drawn on the graph?

  • A𝑦=14(π‘₯+2)βˆ’5
  • B𝑦=βˆ’14(π‘₯+2)+5
  • C𝑦=14(π‘₯+2)+5
  • D𝑦=βˆ’14(π‘₯βˆ’2)+5
  • E𝑦=βˆ’14(π‘₯+2)βˆ’5

Q23:

The figure below represents the function 𝑓(π‘₯)=π‘₯+π‘šοŠ¨. Find the value of π‘š given that the length 𝑂𝐴 is 4 units.

Q24:

The graphs of three quadratic equations are shown on the diagram below. Find the equation for each graph.

  • Ablue: 𝑦=βˆ’π‘₯+1, red: 𝑦=βˆ’π‘₯+4, green: 𝑦=βˆ’π‘₯+9
  • Bblue: 𝑦=βˆ’π‘₯+1,red: 𝑦=βˆ’4π‘₯+4, green: 𝑦=βˆ’9π‘₯+9
  • Cblue: 𝑦=π‘₯βˆ’1, red: 𝑦=4π‘₯βˆ’4, green: 𝑦=9π‘₯βˆ’9
  • Dblue: 𝑦=π‘₯βˆ’1, red: 𝑦=π‘₯βˆ’4, green: 𝑦=π‘₯βˆ’9

Q25:

Describe the sequence of operations on the graph of 𝑦=π‘₯ that produces the graph of 𝑦=π‘₯+π‘Žπ‘₯+π‘οŠ¨.

  • Ashift π‘Ž2 to the right then π‘βˆ’π‘Ž4 up
  • Bshift π‘Ž to the left then π‘βˆ’π‘Ž2 up
  • Cshift π‘Ž2 to the right then π‘βˆ’π‘Ž2 up
  • Dshift π‘Ž2 to the left then π‘βˆ’π‘Ž4 up
  • Eshift π‘Ž2 to the left then π‘βˆ’π‘Ž2 up

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