Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 1 — Questions and Answers
Question 1: What is the standard form of a quadratic equation?
- ax² + bx + c = 0 (Correct answer)
- ax + b = 0
- ax³ + bx² + cx + d = 0
- a/x + b = 0
Correct answer: ax² + bx + c = 0
The standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0.
Question 2: Which of the following is a polynomial expression?
- 3x² + 2x − 5 (Correct answer)
- 3/x + 2
- √x + 4
- x⁻² + 1
Correct answer: 3x² + 2x − 5
A polynomial has non-negative integer exponents, so 3x² + 2x − 5 qualifies.
Question 3: What are the zeros of f(x) = x² − 9?
- x = 3 and x = −3 (Correct answer)
- x = 9 and x = −9
- x = 3 only
- x = 0 and x = 9
Correct answer: x = 3 and x = −3
Setting x² − 9 = 0 gives x² = 9, so x = ±3.
Question 4: What is the vertex of the parabola y = (x − 2)² + 5?
- (2, 5) (Correct answer)
- (−2, 5)
- (2, −5)
- (−2, −5)
Correct answer: (2, 5)
In vertex form y = (x − h)² + k, the vertex is (h, k), so here it is (2, 5).
Question 5: What is the product of (x + 3)(x − 4)?
- x² − x − 12 (Correct answer)
- x² + x − 12
- x² − 12
- x² − 7x − 12
Correct answer: x² − x − 12
Using FOIL: x·x + x·(−4) + 3·x + 3·(−4) = x² − 4x + 3x − 12 = x² − x − 12.
Question 6: Which value of x satisfies x² − 5x + 6 = 0?
- x = 2 and x = 3 (Correct answer)
- x = −2 and x = −3
- x = 1 and x = 6
- x = −1 and x = 6
Correct answer: x = 2 and x = 3
Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 1
What is the standard form of a quadratic equation?