Lesson Worksheet: Roots of Quadratic Functions Mathematics

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

Q1:

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

Q2:

Find the solution set of 5𝑦+24𝑦5=0 in .

  • A{1,5}
  • B{1,5}
  • C{5,5}
  • D15,5
  • E15,5

Q3:

What are the zeros of 𝑓(𝑥)=(𝑥+𝜋)𝑒?

  • A𝜋+𝑒 and 𝜋𝑒
  • B𝑒𝜋 and 𝑒+𝜋
  • C𝜋𝑒 and 𝜋𝑒
  • D𝜋+𝑒 and 𝜋𝑒
  • E𝑒𝜋 and 𝑒+𝜋

Q4:

Find the set of zeros of the function 𝑓(𝑥)=(𝑥2)(𝑥+5)18.

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

Q5:

Which of the following is a solution for 𝑎 given the set of zeros of the function 𝑓(𝑥)=𝑥+𝑎 is empty?

  • A44
  • B44
  • C0
  • D13

Q6:

If a parabola intersects the 𝑥-axis at two points, find the number of roots for the equation in .

  • Aone
  • Bzero
  • Ctwo
  • Dfour
  • Ethree

Q7:

If a parabola touches the 𝑥-axis at a single point, determine the number of roots in .

  • Aone
  • Btwo
  • Cthree
  • Dzero
  • Efour

Q8:

If a parabola does not intersect the 𝑥-axis, determine the number of roots in .

  • Athree
  • Bfour
  • Cone
  • Dzero
  • Etwo

Q9:

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

  • A
  • B
  • C
  • D{0}
  • E

Q10:

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

  1. 𝑓(𝑥)=𝑥+8𝑥+15
  2. 𝑓(𝑥)=(𝑥+4)1
  3. 𝑓(𝑥)=(𝑥+5)(𝑥+3)

Use expression 1 to find the value of 𝑓 when 𝑥=0.

Identify the minimum value of 𝑓 using expression 2.

Identify the zeros of 𝑓 using expression 3.

  • A5, 3
  • B5, 3
  • C8, 15
  • D5, 3
  • E5, 3

Q11:

Find the values of 𝑎 and 𝑏 given the set {4,2} contains the zeros of the function 𝑓(𝑥)=𝑎𝑥+𝑏𝑥32.

  • A𝑎=4, 𝑏=8
  • B𝑎=4, 𝑏=8
  • C𝑎=8, 𝑏=4
  • D𝑎=8, 𝑏=4

Q12:

Find the value of 𝑎, given the set {9} contains the zero of the function 𝑓(𝑥)=𝑥2𝑎𝑥+𝑎.

Q13:

Given that 𝑓(𝑥)=𝑥2𝑥8 and 𝑓(4)=0, find the other root of 𝑓(𝑥).

  • A𝑥=1
  • B𝑥=1
  • C𝑥=4
  • D𝑥=2
  • E𝑥=2

Q14:

Determine the points at which the graph of the function 𝑓𝑓(𝑥)=𝑥𝑥 intersects the 𝑥-axis.

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

Q15:

Find the set of zeros of the function 𝑓(𝑥)=19𝑥.

  • A13
  • B{3}
  • C{3,3}
  • D13
  • E13,13

Q16:

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

  • Azero
  • Bone
  • Can infinite number
  • Dtwo

Q17:

At which values of 𝑥 does the graph of 𝑦=12𝑥8𝑥 cross the 𝑥-axis?

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

Q18:

Find the value of 𝑎 given the set 𝑧(𝑓)={6,8} contains the zeros of the function 𝑓(𝑥)=𝑥14𝑥+𝑎.

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