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
Which of the following represents a function?
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.
What is the vertex of the parabola y = (x − 3)² + 5?
Answer: (3, 5)
In vertex form y = (x − h)² + k, the vertex is (h, k), so h = 3 and k = 5.
If f(x) = 2x² − 3x + 1, what is f(−1)?
Answer: 6
f(−1) = 2(1) − 3(−1) + 1 = 2 + 3 + 1 = 6.
A quadratic equation has discriminant equal to 0. What does this mean?
Answer: One repeated real root
When the discriminant b² − 4ac = 0, there is exactly one repeated (double) real root.
Which equation describes a parabola opening downward?
Answer: y = −3x² + 2x − 1
A parabola opens downward when the coefficient of x² is negative; −3 is negative.
What are the x-intercepts of y = x² − 9?
Answer: x = 3 and x = −3
Setting x² − 9 = 0 gives x² = 9, so x = ±3.
Which value of x satisfies 2x² − 8 = 0?
Answer: x = ±2
2x² = 8 → x² = 4 → x = ±2.