Algebra Test Quadratic Equations 1 — Questions and Answers
Question 1: What are the solutions to x² - 5x + 6 = 0?
- x = 1 and x = 6
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = -1 and x = -6
Correct answer: x = 2 and x = 3
Factor as (x - 2)(x - 3) = 0, giving x = 2 and x = 3.
Question 2: What is the vertex form of a quadratic equation?
- y = ax² + bx + c
- y = a(x - h)² + k (Correct answer)
- y = (ax + b)(cx + d)
- y = mx + b
Correct answer: y = a(x - h)² + k
Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Question 3: What is the discriminant of 2x² - 4x + 2 = 0?
- 0 (Correct answer)
- 8
- -8
- 16
Correct answer: 0
Discriminant = b² - 4ac = (-4)² - 4(2)(2) = 16 - 16 = 0.
Question 4: A discriminant of zero means a quadratic has:
- Two distinct real roots
- No real roots
- One repeated real root (Correct answer)
- Two complex roots
Correct answer: One repeated real root
A discriminant of zero means exactly one repeated real root where the parabola just touches the x-axis.
Question 5: Solve x² - 9 = 0 by factoring.
- x = ±9
- x = ±3 (Correct answer)
- x = 3 only
- x = -3 only
Correct answer: x = ±3
Factor as (x - 3)(x + 3) = 0, giving x = 3 or x = -3.
Question 6: What is the axis of symmetry for y = x² - 6x + 8?
- x = 3 (Correct answer)
- x = -3
- x = 6
- x = -6
Correct answer: x = 3
The axis of symmetry is x = -b/(2a) = -(-6)/(2·1) = 3.
Algebra Test Quadratic Equations 1
What are the solutions to x² - 5x + 6 = 0?