Worksheet: Roots of Quadratic Functions

In this worksheet, we will practice finding the roots of a quadratic from its graph and 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 5 𝑦 + 2 4 𝑦 5 = 0 in .

  • A { 1 , 5 }
  • B 1 5 , 5
  • C { 1 , 5 }
  • D 1 5 , 5
  • E { 5 , 5 }

Q3:

What are the zeros of 𝑓 ( 𝑥 ) = ( 𝑥 + 𝜋 ) 𝑒 2 ?

  • A 𝑒 𝜋 and 𝑒 + 𝜋
  • B 𝜋 + 𝑒 and 𝜋 𝑒
  • C 𝑒 𝜋 and 𝑒 + 𝜋
  • D 𝜋 + 𝑒 and 𝜋 𝑒
  • E 𝜋 𝑒 and 𝜋 𝑒

Q4:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = ( 𝑥 2 ) ( 𝑥 + 5 ) 1 8 .

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

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 1 3
  • B 4 4
  • C0
  • D44

Q6:

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

  • A zero
  • B one
  • C four
  • Dtwo
  • E three

Q7:

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

  • A zero
  • B two
  • C three
  • D one
  • E four

Q8:

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

  • Aone
  • Bthree
  • Ctwo
  • Dzero
  • Efour

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 { 0 }
  • C
  • D
  • E

Q10:

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

  1. 𝑓 ( 𝑥 ) = 𝑥 + 8 𝑥 + 1 5
  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.

  • A8, 15
  • B5, 3
  • C 5 , 3
  • D 5 , 3
  • E 5 , 3

Q11:

Find the values of 𝑎 and 𝑏 given the set { 4 , 2 } contains the zeros of the function 𝑓 ( 𝑥 ) = 𝑎 𝑥 + 𝑏 𝑥 3 2 .

  • A 𝑎 = 4 , 𝑏 = 8
  • B 𝑎 = 8 , 𝑏 = 4
  • C 𝑎 = 8 , 𝑏 = 4
  • D 𝑎 = 4 , 𝑏 = 8

Q12:

Find the value of 𝑎 , given the set { 9 } contains the zero of the function 𝑓 ( 𝑥 ) = 𝑥 2 𝑎 𝑥 + 𝑎 .

Q13:

Given that 𝑓 ( 𝑥 ) = 𝑥 2 𝑥 8 2 and 𝑓 ( 4 ) = 0 , find the other root of 𝑓 ( 𝑥 ) .

  • A 𝑥 = 2
  • B 𝑥 = 4
  • C 𝑥 = 1
  • D 𝑥 = 2
  • E 𝑥 = 1

Q14:

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

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

Q15:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 1 9 𝑥 .

  • A 1 3
  • B 1 3
  • C { 3 , 3 }
  • D 1 3 , 1 3
  • E { 3 }

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 ?

  • A two
  • B one
  • C an infinite number
  • D zero

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