Lesson: Roots of Quadratic Functions

In this lesson, we will learn how to find the roots of a quadratic from its graph and by factoring.

Sample Question Videos

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Worksheet: Roots of Quadratic Functions • 12 Questions • 3 Videos

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 2 in .

Q3:

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

Q4:

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

Q5:

Which of the following is a solution for 𝑎 given the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 + 𝑎 2 is empty?

Q6:

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

Q7:

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

Q8:

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

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 .

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.

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 2 .

Q12:

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

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