Card 1 of 8
MediumStudy card 1
Prompt
What does c reveal in f(x) = ax² + bx + c?
Answer
The y-intercept, f(0).
Quadratic standard form
\[f(x)=ax^2+bx+c\]
MathAdvanced Math
Flashcards
Nonlinear Functions Flashcards
Recall quadratic and exponential features, representations, and distinctions.
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Card 1 of 8. Answer hidden.
Card 2 of 8
MediumStudy card 2
Prompt
What does vertex form reveal immediately?
Answer
The vertex (h, k) and whether the parabola opens up or down from the sign of a.
Quadratic vertex form
\[f(x)=a(x-h)^2+k\]
Card 3 of 8
MediumStudy card 3
Prompt
What does factored form reveal?
Answer
The zeros or x-intercepts, found by setting each factor equal to zero.
Card 4 of 8
MediumStudy card 4
Prompt
In a·bˣ, what does b represent?
Answer
The multiplicative factor for each one-unit increase in x.
Exponential form
\[f(x)=a\cdot b^x\]
Card 5 of 8
MediumStudy card 5
Prompt
How does the exponential base distinguish growth from decay?
Answer
b > 1 gives growth; 0 < b < 1 gives decay.
Card 6 of 8
HardStudy card 6
Prompt
Constant second differences versus constant ratios?
Answer
Constant second differences suggest a quadratic; constant output ratios suggest an exponential.
Card 7 of 8
MediumStudy card 7
Prompt
What does f(x) + k do to a graph?
Answer
It shifts the graph vertically by k units.
Card 8 of 8
MediumStudy card 8
Prompt
What is the key linear-versus-exponential trap?
Answer
Linear change adds a constant amount; exponential change multiplies by a constant factor.
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