Algebra Test Quadratic Equations 2 — Questions and Answers
Question 1: What is the solution to x² = 16?
- x = 4 only
- x = -4 only
- x = ±4 (Correct answer)
- x = ±8
Correct answer: x = ±4
Taking the square root of both sides gives x = ±4.
Question 2: Which correctly factors 3x² + 9x?
- 3(x² + 9x)
- 3x(x + 3) (Correct answer)
- x(3x + 9)
- 3x(3x + 3)
Correct answer: 3x(x + 3)
Factor out the GCF of 3x to get 3x(x + 3).
Question 3: For the parabola y = -2x² + 4x - 1, which direction does it open?
- Upward
- Downward (Correct answer)
- Left
- Right
Correct answer: Downward
Since the leading coefficient a = -2 is negative, the parabola opens downward.
Question 4: What is the solution set of x² + 4x + 4 = 0?
- x = 2 and x = -2
- x = 2
- x = -2 (Correct answer)
- x = 4
Correct answer: x = -2
Factor as (x + 2)² = 0, giving x = -2 as a double root.
Question 5: Using the quadratic formula, solve x² - 2x - 3 = 0.
- x = 3 and x = -1 (Correct answer)
- x = -3 and x = 1
- x = 1 and x = -2
- x = 2 and x = -1
Correct answer: x = 3 and x = -1
Using x = (2 ± √(4 + 12))/2 = (2 ± 4)/2 gives x = 3 or x = -1.
Question 6: What is the vertex of y = (x - 3)² + 5?
- (3, 5) (Correct answer)
- (-3, 5)
- (3, -5)
- (-3, -5)
Correct answer: (3, 5)
In vertex form y = a(x - h)² + k, the vertex is (h, k) = (3, 5).
Algebra Test Quadratic Equations 2
What is the solution to x² = 16?