3.05 Analyzing Quadratic Equations

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Analyzing Quadratic Equations Review

Let's see what you know about discriminants.

1. Given the graph of the function, determine if the discriminant is less than zero, equal to zero, or greater than zero.

   

   1. D = 0
   2. D < 0
   3. D > 0

   Answer: c. D > 0. The graph has two x intercepts, so it must have a discrimiant that is positive.

2. Given x² − 10x + 25, determine if the roots are real or imaginary.
   1. real and imaginary
   2. imaginary
   3. real

   Answer: c. real. Since the discriminant is greater than or equation to zero, the root must be real.

3. Given x² − 2x + 1 = 0, determine the number of x-intercepts.
   1. 1
   2. 2

   Answer: a. 1. Since the discriminant is equal to zero, there is one real double root.

4. If the discriminant of an equation is 4, which of the following is true?
   1. there are 2 real roots
   2. there are 2 imaginary roots

   Answer: b. there are 2 real roots. Because the discriminant is positive, there must be two real roots.

5. Given −x² − 3x − 5 = 0, determine if the roots are real or imaginary.
   1. imaginary
   2. real

   Answer: b. imaginary. Since the discriminant is negative, the roots must be imaginary.

6. Given the graph of the function, determine if the discriminant is less than zero, equal to zero, or greater than zero.

   

   1. D = 0
   2. D < 0
   3. D > 0

   Answer: b. D < 0. The graph has 0 x-intercepts, so the discriminant must be less than zero.

7. Given the graph of the function, determine if the discriminant is less than zero, equal to zero, or greater than zero.

   

   1. D = 0
   2. D < 0
   3. D > 0

   Answer: c. D > 0. The graph has two x-intercepts, so it must have a discriminant that is positive.

8. If the discriminant of an equation is −3, which of the following is true?
   1. there are 2 real roots
   2. there are 2 imaginary roots

   Answer: c. there are 2 imaginary roots. Since the dsicriminant is negative, there must be two imaginary roots.

9. Given x² + 3x − 1 = 0, determine the number of x-intercepts.
   1. 1
   2. 2

   Answer: b. 2. Since the discriminant is positive, there are two real roots and 2 x-intercepts.

10. Given the graph of the function, determine if the discriminant is less than zero, equal to zero, or greater than zero.

    

    1. D = 0
    2. D < 0
    3. D > 0

    Answer: a. D = 0. The graph has 0 x-intercepts, so the discriminant must be less than zero.