Question

A graph of quadratic function y = f(x) is shown below.

mc005-1.jpg

What is the solution set of the quadratic inequality mc005-2.jpg?
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mc005-4.jpg
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Answer 1

I don’t have the images or the exact inequality text, so I can’t give the specific interval(s) yet. Could you either

- upload the two images (the graph and the inequality), or
- type here the inequality (for example “f(x) ≥ 2”) and give the graph details: vertex, x‑intercepts (if any), where the parabola opens, and any points of intersection with a horizontal line y = k if that’s shown?

Meanwhile, here’s how to solve these problems so you can check quickly:

1. Identify the inequality type:
- If it’s f(x) > 0 or f(x) < 0 (or ≥ / ≤), you are comparing the graph to the x‑axis.
- If it’s f(x) > k or f(x) < k (or ≥ / ≤), compare the graph to the horizontal line y = k.

2. Draw (or imagine) the horizontal line y = k (where k is 0 if not given). Find the x‑coordinates of all intersection points between the parabola and that line by solving f(x) = k (graphically these are the x-values where the curve crosses the line).

3. Use the graph to determine where the parabola is above or below that line:
- For f(x) > k: take the x-intervals where the curve lies strictly above the line.
- For f(x) ≥ k: include points of intersection as well.
- For f(x) < k or ≤ : analogous, for where curve is strictly below or below-or-on the line.

4. Express the solution as a union of intervals, using parentheses for strict inequalities and brackets for inclusive ones.

Example: If the parabola opens upward, crosses y = 0 at x = −2 and x = 3, then
- f(x) > 0 on (−∞, −2) ∪ (3, ∞)
- f(x) < 0 on (−2, 3)
- f(x) ≥ 0 on (−∞, −2] ∪ [3, ∞)
- f(x) ≤ 0 on [−2, 3]

Send the graph or the exact inequality and I’ll compute the precise solution set.