MPT College Algebra 2 — Questions and Answers
Question 1: Which of the following is the vertex of the parabola y = 2(x - 3)² + 5?
- (3, 5) (Correct answer)
- (-3, 5)
- (3, -5)
- (-3, -5)
Correct answer: (3, 5)
The vertex form y = a(x - h)² + k gives vertex (h, k) = (3, 5).
Question 2: If f(x) = 3x² - 2x + 1, what is f(-2)?
- 17 (Correct answer)
- 9
- 21
- 13
Correct answer: 17
f(-2) = 3(4) - 2(-2) + 1 = 12 + 4 + 1 = 17.
Question 3: Solve the inequality: 2x - 5 > 3. Which answer correctly expresses the solution?
- x > 4 (Correct answer)
- x > -1
- x < 4
- x > 8
Correct answer: x > 4
Add 5 to both sides: 2x > 8, then divide by 2: x > 4.
Question 4: What are the roots of 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
Factor as (x - 2)(x - 3) = 0, giving roots x = 2 and x = 3.
Question 5: Which expression is equivalent to log₂(8) + log₂(4)?
- 5 (Correct answer)
- 7
- 32
- 12
Correct answer: 5
log₂(8) = 3 and log₂(4) = 2, so their sum is 5.
Question 6: A line passes through (1, 2) and (4, 8). What is its slope?
- 2 (Correct answer)
- 1/2
- 3
- 6
Correct answer: 2
Slope = (8 - 2)/(4 - 1) = 6/3 = 2.
Question 7: Simplify: (x³y²)/(x⁻¹y⁴)
- x⁴/y² (Correct answer)
- x²y²
- x⁴y⁶
- x²/y²
Correct answer: x⁴/y²
Divide exponents: x^(3-(-1)) = x⁴ and y^(2-4) = y⁻² = 1/y².
MPT College Algebra 2
Which of the following is the vertex of the parabola y = 2(x - 3)² + 5?