Rise Placement Test Functions and Quadratic Equations 2 — Questions and Answers
Question 1: Which of the following represents a function?
- A circle centered at the origin
- {(1,2),(1,3),(2,4)}
- {(1,2),(2,3),(3,4)} (Correct answer)
- x² + y² = 9
Correct answer: {(1,2),(2,3),(3,4)}
A relation is a function if each input (x-value) maps to exactly one output, which only {(1,2),(2,3),(3,4)} satisfies.
Question 2: What is the vertex of the parabola y = (x − 3)² + 5?
- (−3, 5)
- (3, −5)
- (3, 5) (Correct answer)
- (−3, −5)
Correct answer: (3, 5)
In vertex form y = (x − h)² + k, the vertex is (h, k), so h = 3 and k = 5.
Question 3: If f(x) = 2x² − 3x + 1, what is f(−1)?
- 6 (Correct answer)
- −4
- 0
- 2
Correct answer: 6
f(−1) = 2(1) − 3(−1) + 1 = 2 + 3 + 1 = 6.
Question 4: A quadratic equation has discriminant equal to 0. What does this mean?
- Two distinct real roots
- One repeated real root (Correct answer)
- Two complex roots
- No solution
Correct answer: One repeated real root
When the discriminant b² − 4ac = 0, there is exactly one repeated (double) real root.
Question 5: Which equation describes a parabola opening downward?
- y = x² + 4
- y = −3x² + 2x − 1 (Correct answer)
- y = (x+1)²
- y = 3x² − 5
Correct answer: y = −3x² + 2x − 1
A parabola opens downward when the coefficient of x² is negative; −3 is negative.
Question 6: What are the x-intercepts of y = x² − 9?
- x = 9 and x = −9
- x = 3 only
- x = 3 and x = −3 (Correct answer)
- x = ±√3
Correct answer: x = 3 and x = −3
Setting x² − 9 = 0 gives x² = 9, so x = ±3.
Question 7: Which value of x satisfies 2x² − 8 = 0?
- x = ±4
- x = ±2 (Correct answer)
- x = 2 only
- x = 4 only
Correct answer: x = ±2
2x² = 8 → x² = 4 → x = ±2.
Rise Placement Test Functions and Quadratic Equations 2
Which of the following represents a function?