Although the exact value of a cannot be determined from the graph alone, we know that it is negative.
It lies between 0 and the smaller x-intercept (where f(x) = 0).
1. Identify the intercepts:
- From the graph, we can see that the y-intercept (where the graph crosses the y-axis) is at (0, 10).
- This means that when x = 0, f(x) = 10.
2. Analyze the behavior near the intercepts:
- The graph appears to curve downwards to the right of the y-intercept, suggesting that f(x) decreases as x increases beyond 0.
- Therefore, the value of a must be negative for f(x) to reach 0 at some point.
3. Look for the x-axis crossings:
- The graph crosses the x-axis (where f(x) = 0) at two points.
- Let these points be (a, 0) and (b, 0), where a < b (since the graph decreases as x increases).
4. Utilize the information from the intercepts and crossings:
- We know that f(0) = 10 and f(a) = 0.
- Since f(x) is continuous (no abrupt jumps or gaps in the graph), there must be a point between 0 and a where the function reaches its maximum value of 10.
- This means that the equation f(x) = 10 has two solutions: x = 0 and x = some value between 0 and a.
5. Determine the value of a:
- Since f(a) = 0 and a is the smaller x-intercept, it follows that a must be negative.
- The negative value of a ensures that the function reaches its maximum value of 10 before crossing the x-axis at a.