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 axis of symmetry for y = 2x² − 12x + 7?
Answer: x = 3
The axis of symmetry is x = −b/(2a) = −(−12)/(2·2) = 3.
The function f(x) = x² − 2x − 15 crosses the x-axis at which points?
Answer: x = 5 and x = −3
Factoring gives (x−5)(x+3) = 0, so x = 5 or x = −3.
If f(x) = 3x + 2 and g(x) = x², what is f(g(2))?
Answer: 14
g(2) = 4, then f(4) = 3(4) + 2 = 14.
How many real solutions does 3x² + 2x + 5 = 0 have?
Answer: No real solutions
The discriminant is 4 − 60 = −56 < 0, so there are no real solutions.
Which point is on the graph of f(x) = x² − 3x + 2?
Answer: (1, 0)
f(1) = 1 − 3 + 2 = 0, so (1, 0) is on the graph.
Which form of a quadratic equation makes it easiest to identify the roots?
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.
The parabola y = ax² + bx + c has its vertex at (−1, 4) and passes through (1, 0). What is the value of a?
Answer: a = −1
Using vertex form y = a(x+1)² + 4 and point (1,0): 0 = a(4) + 4 → a = −1.