Worksheet: Roots of Quadratic Functions

In this worksheet, we will practice solving quadratic equations by factoring.

Q1:

Given that 𝑓(π‘₯) is a quadratic function and π‘₯=4 is a root of the equation 𝑓(π‘₯)=0, what is the value of 𝑓(4)?

Q2:

Find the solution set of 5𝑦+24π‘¦βˆ’5=0 in ℝ.

  • A { 1 , βˆ’ 5 }
  • B { βˆ’ 1 , 5 }
  • C { 5 , βˆ’ 5 }
  • D  βˆ’ 1 5 , 5 
  • E  1 5 , βˆ’ 5 

Q3:

What are the zeros of 𝑓(π‘₯)=(π‘₯+πœ‹)βˆ’π‘’οŠ¨?

  • A βˆ’ πœ‹ + √ 𝑒 and βˆ’πœ‹βˆ’βˆšπ‘’
  • B √ 𝑒 βˆ’ πœ‹ and βˆšπ‘’+πœ‹
  • C βˆ’ πœ‹ βˆ’ √ 𝑒 and βˆ’πœ‹βˆ’βˆšπ‘’
  • D βˆ’ πœ‹ + 𝑒 and βˆ’πœ‹βˆ’π‘’
  • E 𝑒 βˆ’ πœ‹ and 𝑒+πœ‹

Q4:

Find the set of zeros of the function 𝑓(π‘₯)=(π‘₯βˆ’2)(π‘₯+5)βˆ’18.

  • A { 2 , βˆ’ 5 }
  • B { βˆ’ 7 , 4 }
  • C { βˆ’ 7 , βˆ’ 4 }
  • D { 7 , βˆ’ 4 }
  • E { 7 , 4 }

Q5:

Which of the following is a solution for π‘Ž given the set of zeros of the function 𝑓(π‘₯)=π‘₯+π‘ŽοŠ¨ is empty?

  • A βˆ’ 4 4
  • B44
  • C0
  • D βˆ’ 1 3

Q6:

If a parabola intersects the π‘₯-axis at two points, find the number of roots for the equation in ℝ.

  • Aone
  • Bzero
  • Ctwo
  • Dfour
  • Ethree

Q7:

If a parabola touches the π‘₯-axis at a single point, determine the number of roots in ℝ.

  • Aone
  • Btwo
  • Cthree
  • Dzero
  • Efour

Q8:

If a parabola does not intersect the π‘₯-axis, determine the number of roots in ℝ.

  • Athree
  • Bfour
  • Cone
  • Dzero
  • Etwo

Q9:

Given the curve of the quadratic function 𝑓 does not intersect the π‘₯-axis, determine 𝑍(𝑓). Recall that 𝑍(𝑓) is the set of zeros of the function 𝑓.

  • A βˆ…
  • B β„š
  • C β„•
  • D { 0 }
  • E ℝ

Q10:

The following expressions are equivalent ways of writing the function 𝑓.

  1. 𝑓 ( π‘₯ ) = π‘₯ + 8 π‘₯ + 1 5 
  2. 𝑓 ( π‘₯ ) = ( π‘₯ + 4 ) βˆ’ 1 
  3. 𝑓 ( π‘₯ ) = ( π‘₯ + 5 ) ( π‘₯ + 3 )

Use expression 1 to find the value of 𝑓 when π‘₯=0.

Identify the minimum value of 𝑓 using expression 2.

Identify the zeros of 𝑓 using expression 3.

  • A βˆ’ 5 , 3
  • B5, 3
  • C8, 15
  • D βˆ’ 5 , βˆ’ 3
  • E5, βˆ’3

Q11:

Find the values of π‘Ž and 𝑏 given the set {βˆ’4,2} contains the zeros of the function 𝑓(π‘₯)=π‘Žπ‘₯+𝑏π‘₯βˆ’32.

  • A π‘Ž = 4 , 𝑏 = 8
  • B π‘Ž = βˆ’ 4 , 𝑏 = βˆ’ 8
  • C π‘Ž = 8 , 𝑏 = 4
  • D π‘Ž = βˆ’ 8 , 𝑏 = βˆ’ 4

Q12:

Find the value of π‘Ž, given the set {βˆ’9} contains the zero of the function 𝑓(π‘₯)=π‘₯βˆ’2π‘Žπ‘₯+π‘ŽοŠ¨οŠ¨.

Q13:

Given that 𝑓(π‘₯)=π‘₯βˆ’2π‘₯βˆ’8 and 𝑓(4)=0, find the other root of 𝑓(π‘₯).

  • A π‘₯ = 1
  • B π‘₯ = βˆ’ 1
  • C π‘₯ = βˆ’ 4
  • D π‘₯ = 2
  • E π‘₯ = βˆ’ 2

Q14:

Determine the points at which the graph of the function π‘“βˆΆπ‘“(π‘₯)=π‘₯βˆ’π‘₯ intersects the π‘₯-axis.

  • A ( 2 , 0 ) , ( 0 , 1 )
  • B ( 2 , 0 ) , ( βˆ’ 1 , 0 )
  • C ( 0 , 0 ) , ( 1 , 0 )
  • D ( 0 , 0 ) , ( βˆ’ 1 , 0 )

Q15:

Find the set of zeros of the function 𝑓(π‘₯)=1βˆ’9π‘₯.

  • A  βˆ’ 1 3 
  • B { 3 }
  • C { 3 , βˆ’ 3 }
  • D  1 3 
  • E  1 3 , βˆ’ 1 3 

Q16:

If the graph of the quadratic function, 𝑓(π‘₯), does not intersect the π‘₯-axis, how many solutions are there to the equation 𝑓(π‘₯)=0?

  • Azero
  • Bone
  • Can infinite number
  • Dtwo

Q17:

At which values of π‘₯ does the graph of 𝑦=12π‘₯βˆ’8π‘₯ cross the π‘₯-axis?

  • A0 and 23
  • B0 and βˆ’83
  • C0 and βˆ’23
  • D0 and 83
  • E0 and 2

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