QUADRATIC FUNCTION SUMMARY
| QUADRATIC FUNCTION SUMMARY | ||||||
| STANDARD FORM: f(x) = ax^2 + bx + c | ||||||
| Domain | Graph (shape) |
Vertex | Range | yintercept | xintercept( s) |
|
| a > 0 | all real numbers * |
 |
Lowest point (-b/2a, f(-b/2a) |
f(-b/2a) to infinity |
(0, c) | solutions to f (x) = 0  |
| a < 0 | all real numbers * |
 |
Highest point (-b/2a, f(-b/2a) |
negative infinity to f(-b/2a) |
(0, c) | solutions to f (x) = 0  |
| VERTEX FORM : f(x) = a(x – h)^2 + k | ||||||
| a > 0 | all real numbers* |
 |
(h, k) | k to infinity | (0, ah^2 +k) | solutions to f(x) = 0 ( Use square root solution method ) |
| a < 0 | all real numbers* |
 |
(h, k) | negative infinity to k |
(0, ah^2 +k) | solutions to f(x) = 0 ( Use square root solution method ) |
| * A quadratic function used as a physical model may have restrictions. | ||||||
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