Rise Placement Test Functions and Quadratic Equations 4 — Questions and Answers
Question 1: What is the axis of symmetry for y = 2x² − 12x + 7?
- x = 3 (Correct answer)
- x = −3
- x = 6
- x = −6
Correct answer: x = 3
The axis of symmetry is x = −b/(2a) = −(−12)/(2·2) = 3.
Question 2: The function f(x) = x² − 2x − 15 crosses the x-axis at which points?
- x = 5 and x = −3 (Correct answer)
- x = −5 and x = 3
- x = 5 and x = 3
- x = −5 and x = −3
Correct answer: x = 5 and x = −3
Factoring gives (x−5)(x+3) = 0, so x = 5 or x = −3.
Question 3: If f(x) = 3x + 2 and g(x) = x², what is f(g(2))?
- 14 (Correct answer)
- 10
- 16
- 8
Correct answer: 14
g(2) = 4, then f(4) = 3(4) + 2 = 14.
Question 4: How many real solutions does 3x² + 2x + 5 = 0 have?
- Two real solutions
- One real solution
- No real solutions (Correct answer)
- Infinitely many
Correct answer: No real solutions
The discriminant is 4 − 60 = −56 < 0, so there are no real solutions.
Question 5: Which point is on the graph of f(x) = x² − 3x + 2?
- (0, 3)
- (1, 0) (Correct answer)
- (2, 2)
- (3, 5)
Correct answer: (1, 0)
f(1) = 1 − 3 + 2 = 0, so (1, 0) is on the graph.
Question 6: Which form of a quadratic equation makes it easiest to identify the roots?
- Standard form: ax² + bx + c = 0
- Vertex form: a(x−h)² + k
- Factored form: a(x−r₁)(x−r₂) (Correct answer)
- Slope-intercept form: y = mx + b
Correct answer: Factored form: a(x−r₁)(x−r₂)
In factored form a(x−r₁)(x−r₂), the roots are immediately visible as r₁ and r₂.
Question 7: The parabola y = ax² + bx + c has its vertex at (−1, 4) and passes through (1, 0). What is the value of a?
- a = −1 (Correct answer)
- a = −4
- a = 1
- a = 4
Correct answer: a = −1
Using vertex form y = a(x+1)² + 4 and point (1,0): 0 = a(4) + 4 → a = −1.
Rise Placement Test Functions and Quadratic Equations 4
What is the axis of symmetry for y = 2x² − 12x + 7?