Lesson Worksheet: Quadratic Functions in Different Forms Mathematics

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


Rewrite the expression 𝑥+14𝑥 in the form (𝑥+𝑝)+𝑞.

  • A(𝑥+7)49
  • B(𝑥14)+196
  • C(𝑥7)+49
  • D(𝑥7)49
  • E(𝑥+14)196

What is the minimum value of the function 𝑓(𝑥)=𝑥+14𝑥?


Find the vertex of the graph of 𝑦=𝑥.

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


Find the vertex of the graph of 𝑦=5(𝑥+1)+6.

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


Consider the graph:

Which is the following is the same as the function 𝑓(𝑥)=2(𝑥+1)(𝑥+5) whose graph is shown?

  • A𝑓(𝑥)=2(𝑥3)+8
  • B𝑓(𝑥)=2(𝑥+3)4
  • C𝑓(𝑥)=2(𝑥+3)+8
  • D𝑓(𝑥)=2(𝑥+3)8
  • E𝑓(𝑥)=2(𝑥3)+4


Determine the quadratic function 𝑓 with the following properties:

  • its graph has a vertex at (3,17)
  • 𝑓(4)=5
  • A𝑓(𝑥)=22(𝑥3)+17
  • B𝑓(𝑥)=22(𝑥3)17
  • C𝑓(𝑥)=17(𝑥3)17
  • DThe function does not exist.
  • E𝑓(𝑥)=22(𝑥+3)17


By writing 𝑓(𝑥)=𝑥+8𝑥+𝐴 in vertex form, find 𝐴 such that 𝑓(𝑥)=3 has exactly one solution.

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


Consider the function 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+𝑐 where 𝑎0. What is the 𝑥-coordinate of the vertex of its curve?

  • A𝑏2𝑎
  • B𝑏2𝑎
  • C𝑎2𝑏
  • D𝑎2𝑏


Find the vertex of the graph of 𝑦=(𝑥3)+2.

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


Rewrite the expression 4𝑥12𝑥+13 in the form 𝑎(𝑥+𝑝)+𝑞.

  • A4𝑥34+2
  • B4𝑥32+4
  • C4(𝑥+3)23
  • D4𝑥+32+4
  • E4(𝑥3)23

What is the minimum value of the function 𝑓(𝑥)=4𝑥12𝑥+13?


Rewrite the expression 𝑥12𝑥+20 in the form (𝑥+𝑝)+𝑞.

  • A(𝑥6)16
  • B(𝑥12)+20
  • C(𝑥+6)16
  • D(𝑥12)20
  • E(𝑥6)+16

What is the minimum value of the function 𝑓(𝑥)=𝑥12𝑥+20?

This lesson includes 10 additional questions and 30 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.