Lesson Worksheet: Quadratic Functions in Different Forms Mathematics • 9th Grade

In this worksheet, we will practice evaluating and writing a quadratic function in different forms.


Rewrite the expression π‘₯+14π‘₯ in the form (π‘₯+𝑝)+π‘žοŠ¨.

  • A(π‘₯+7)βˆ’49
  • B(π‘₯βˆ’14)+196
  • C(π‘₯βˆ’7)+49
  • D(π‘₯βˆ’7)βˆ’49
  • E(π‘₯+14)βˆ’196

What is the minimum value of the function 𝑓(π‘₯)=π‘₯+14π‘₯?


Find the vertex of the graph of 𝑦=βˆ’π‘₯.

  • A(0,1)
  • B(0,0)
  • C(βˆ’1,βˆ’1)
  • D(1,0)
  • E(1,1)


Find the vertex of the graph of 𝑦=5(π‘₯+1)+6.

  • A(6,βˆ’1)
  • B(βˆ’1,βˆ’6)
  • C(βˆ’1,6)
  • D(1,6)
  • E(6,1)


Consider the graph:

Which is the following is the same as the function 𝑓(π‘₯)=βˆ’2(π‘₯+1)(π‘₯+5) whose graph is shown?

  • A𝑓(π‘₯)=2(π‘₯βˆ’3)+8
  • B𝑓(π‘₯)=βˆ’2(π‘₯+3)βˆ’4
  • C𝑓(π‘₯)=βˆ’2(π‘₯+3)+8
  • D𝑓(π‘₯)=2(π‘₯+3)βˆ’8
  • E𝑓(π‘₯)=βˆ’2(π‘₯βˆ’3)+4


Determine the quadratic function 𝑓 with the following properties:

  • its graph has a vertex at (3,βˆ’17)
  • 𝑓(4)=5
  • A𝑓(π‘₯)=22(π‘₯βˆ’3)+17
  • B𝑓(π‘₯)=22(π‘₯βˆ’3)βˆ’17
  • C𝑓(π‘₯)=17(π‘₯βˆ’3)βˆ’17
  • DThe function does not exist.
  • E𝑓(π‘₯)=22(π‘₯+3)βˆ’17


By writing 𝑓(π‘₯)=βˆ’π‘₯+8π‘₯+𝐴 in vertex form, find 𝐴 such that 𝑓(π‘₯)=3 has exactly one solution.

  • A𝐴=20
  • B𝐴=βˆ’20
  • C𝐴=βˆ’13
  • D𝐴=βˆ’33
  • E𝐴=13


Consider the function 𝑓(π‘₯)=π‘Žπ‘₯+𝑏π‘₯+π‘οŠ¨ where π‘Žβ‰ 0. What is the π‘₯-coordinate of the vertex of its curve?

  • A𝑏2π‘Ž
  • Bβˆ’π‘2π‘Ž
  • Cβˆ’π‘Ž2𝑏
  • Dπ‘Ž2𝑏


Find the vertex of the graph of 𝑦=(π‘₯βˆ’3)+2.

  • A(βˆ’3,2)
  • B(2,βˆ’3)
  • C(βˆ’2,3)
  • D(2,3)
  • E(3,2)


Rewrite the expression 4π‘₯βˆ’12π‘₯+13 in the form π‘Ž(π‘₯+𝑝)+π‘žοŠ¨.

  • A4ο€Όπ‘₯βˆ’34+2
  • B4ο€Όπ‘₯βˆ’32+4
  • C4(π‘₯+3)βˆ’23
  • D4ο€Όπ‘₯+32+4
  • E4(π‘₯βˆ’3)βˆ’23

What is the minimum value of the function 𝑓(π‘₯)=4π‘₯βˆ’12π‘₯+13?


Rewrite the expression π‘₯βˆ’12π‘₯+20 in the form (π‘₯+𝑝)+π‘žοŠ¨.

  • A(π‘₯βˆ’6)βˆ’16
  • B(π‘₯βˆ’12)+20
  • C(π‘₯+6)βˆ’16
  • D(π‘₯βˆ’12)βˆ’20
  • E(π‘₯βˆ’6)+16

What is the minimum value of the function 𝑓(π‘₯)=π‘₯βˆ’12π‘₯+20?

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