Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 2 — Questions and Answers
Question 1: Which method can be used to find the roots of any quadratic equation?
- Quadratic formula (Correct answer)
- Only factoring
- Only graphing
- Long division
Correct answer: Quadratic formula
The quadratic formula x = (−b ± √(b²−4ac)) / 2a works for any quadratic equation.
Question 2: What does the discriminant b² − 4ac tell you about a quadratic equation?
- The number and type of solutions (Correct answer)
- The vertex of the parabola
- The y-intercept
- The axis of symmetry
Correct answer: The number and type of solutions
The discriminant determines if there are two real, one real, or two complex solutions.
Question 3: What is the axis of symmetry of y = 2x² − 8x + 3?
- x = 2 (Correct answer)
- x = −2
- x = 4
- x = 8
Correct answer: x = 2
The axis of symmetry is x = −b/(2a) = −(−8)/(2·2) = 8/4 = 2.
Question 4: Which of the following correctly factors 2x² + 7x + 3?
- (2x + 1)(x + 3) (Correct answer)
- (2x + 3)(x + 1)
- (x + 3)(x + 1)
- (2x − 1)(x − 3)
Correct answer: (2x + 1)(x + 3)
Expanding (2x + 1)(x + 3) = 2x² + 6x + x + 3 = 2x² + 7x + 3.
Question 5: A parabola opens downward when the leading coefficient a is:
- Negative (Correct answer)
- Positive
- Zero
- Equal to 1
Correct answer: Negative
When a < 0 in y = ax² + bx + c, the parabola opens downward.
Question 6: What is the degree of the polynomial 4x³ − 2x² + x − 7?
- 3 (Correct answer)
- 4
- 2
- 1
Correct answer: 3
The degree is the highest exponent, which is 3 in 4x³.
Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 2
Which method can be used to find the roots of any quadratic equation?