Lesson Worksheet: Roots of Quadratic Functions Mathematics

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


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)?


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

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


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


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}


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


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

  • Aone
  • Bzero
  • Ctwo
  • Dfour
  • Ethree


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

  • Aone
  • Btwo
  • Cthree
  • Dzero
  • Efour


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

  • Athree
  • Bfour
  • Cone
  • Dzero
  • Etwo


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


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

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