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Worksheet: Roots of Quadratic Functions

Q1:

Find the solution set of 5 𝑦 + 2 4 𝑦 βˆ’ 5 = 0 2 in ℝ .

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

Q2:

What are the zeros of 𝑓 ( π‘₯ ) = ( π‘₯ + πœ‹ ) βˆ’ 𝑒 2 ?

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

Q3:

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

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

Q4:

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

Q5:

Which of the following is a solution for π‘Ž given the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ + π‘Ž 2 is empty?

  • A βˆ’ 1 3
  • B βˆ’ 4 4
  • C0
  • D44

Q6:

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

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

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

Q7:

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

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

Q8:

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

  • Aone
  • Bthree
  • Ctwo
  • Dzero
  • Efour

Q9:

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 ) ?

Q10:

Find the values of π‘Ž and 𝑏 given the set { βˆ’ 4 , 2 } contains the zeros of the function 𝑓 ( π‘₯ ) = π‘Ž π‘₯ + 𝑏 π‘₯ βˆ’ 3 2 2 .

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

Q11:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 2 ) ( π‘₯ + 5 ) βˆ’ 1 8 .

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

Q12:

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