a, q, and the Number of x-intercepts
Completion requirements
Using both Example 1 and the Investigation, you can summarize how to determine the number of \(x\)-intercepts depending on the values of \(a\) and \(q\). Use your graphing calculator to visualize the table, using the examples provided.
\(a\), \(q\), and the number of \(x\)-intercepts
| Key Lesson Marker |
\(a\), \(q\), and the number of \(x\)-intercepts
| \(a\) | \(q\) |
Number of
\(x\)-intercepts |
Example | Screen Shot |
|---|---|---|---|---|
|
\(a < 0 \)
(opens downward) |
\(q < 0 \) | none |
\(f(x) = -(x - 3)^2 - 4 \)
|
|
| \(q = 0 \) | one | \(f(x) = -(x - 3)^2 \) | 
|
|
| \(q > 0 \) | two | \(f(x) = -(x - 3)^2 + 4 \) | 
|
|
|
\(a > 0 \)
(opens upward) |
\(q < 0 \) | two | \(f(x) = (x - 3)^2 - 4 \) | 
|
| \(q = 0 \) | one | \(f(x) = (x - 3)^2 \) | 
|
|
| \(q > 0 \) | none | \(f(x) = (x - 3)^2 + 4 \) | 
|