Functions and Quadratic Equations Flashcards
7 cards from real Rise Placement Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Functions and Quadratic Equations flashcards as text
What is the minimum value of f(x) = x² − 6x + 10?
Answer: 1
Completing the square: f(x) = (x−3)² + 1, so the minimum value is 1 at x = 3.
Which equation has roots x = 4 and x = −1?
Answer: x² − 3x − 4 = 0
(x−4)(x+1) = x² − 3x − 4 = 0 has roots x = 4 and x = −1.
A function f is defined as f(x) = x² for x ≥ 0. What is its inverse function?
Answer: f⁻¹(x) = √x
Swapping x and y in y = x² gives x = y², so y = √x for x ≥ 0.
Completing the square on x² + 8x gives:
Answer: (x + 4)² − 16
x² + 8x = (x+4)² − 16 by adding and subtracting (8/2)² = 16.
The height of a projectile is given by h = −5t² + 20t + 25. What is the initial height (t = 0)?
Answer: 25 m
At t = 0: h = −5(0) + 20(0) + 25 = 25 meters.
If f(x) = x² + 1 and g(x) = 2x − 3, what is (f ∘ g)(1)?
Answer: 2
g(1) = 2(1) − 3 = −1, then f(−1) = (−1)² + 1 = 2.
For the equation y = 2(x − 1)² − 8, what are the x-intercepts?
Answer: x = 3 and x = −1
Setting y = 0: 2(x−1)² = 8 → (x−1)² = 4 → x − 1 = ±2 → x = 3 or x = −1.