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+24𝑦−5=0 in ℝ.

  • A{1,−5}
  • B{−1,5}
  • C{5,−5}
  • D−15,5
  • E15,−5

Q3:

What are the zeros of 𝑓(𝑥)=(𝑥+𝜋)−𝑒?

  • A−𝜋+√𝑒 and −𝜋−√𝑒
  • B√𝑒−𝜋 and √𝑒+𝜋
  • C−𝜋−√𝑒 and −𝜋−√𝑒
  • D−𝜋+𝑒 and −𝜋−𝑒
  • E𝑒−𝜋 and 𝑒+𝜋

Q4:

Find the set of zeros of the function 𝑓(𝑥)=(𝑥−2)(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?

  • A−44
  • B44
  • C0
  • D−13

Q6:

If a parabola intersects the 𝑥-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 𝑥-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 𝑥-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 𝑥-axis, determine 𝑍(𝑓). Recall that 𝑍(𝑓) is the set of zeros of the function 𝑓.

  • A∅
  • Bℚ
  • Cℕ
  • D{0}
  • Eℝ

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.

  • A−5, 3
  • B5, 3
  • C8, 15
  • D−5, −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+𝑏𝑥−32.

  • 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)=𝑥−2𝑎𝑥+𝑎.

Q13:

Given that 𝑓(𝑥)=𝑥−2𝑥−8 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 𝑓∶𝑓(𝑥)=𝑥−𝑥 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)=1−9𝑥.

  • A−13
  • 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=12𝑥−8𝑥 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)=𝑥−14𝑥+𝑎.

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