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
Using the quadratic formula, what are the solutions to x² + 4x + 3 = 0?
Answer: x = −1 and x = −3
Factoring gives (x+1)(x+3) = 0, so x = −1 or x = −3.
What is the domain of f(x) = √(x − 4)?
Answer: x ≥ 4
The expression under the square root must be non-negative, so x − 4 ≥ 0, giving x ≥ 4.
If g(x) = x² − 4x + 4, what is g(x) in factored form?
Answer: (x − 2)²
x² − 4x + 4 is a perfect square trinomial equal to (x − 2)².
A ball is thrown upward with height h(t) = −16t² + 64t. At what time does it reach its maximum height?
Answer: t = 2 sec
The vertex time is t = −b/(2a) = −64/(2·(−16)) = 2 seconds.
Which transformation moves the graph of f(x) = x² three units to the right?
Answer: f(x) = (x−3)²
Replacing x with (x − 3) shifts the graph 3 units to the right.
What is the range of f(x) = −x² + 6?
Answer: y ≤ 6
Since the parabola opens downward with vertex at (0,6), the maximum value is 6, so y ≤ 6.
Which of the following is NOT a quadratic function?
Answer: y = 5x − 7
y = 5x − 7 is a linear function, not quadratic, because it has no x² term.