Question

The graph below represents the solution set of which inequality?
mc013-1.jpg
x2 – 2x – 8 < 0
x2 + 2x – 8 < 0
x2 – 2x – 8 > 0
x2 + 2x – 8 > 0

Answer 1

I can't see the image you attached. Could you upload it again or describe the number line (where the open/closed dots are and which region is shaded)?

Meanwhile, here's how to match the graph to the correct inequality:

- x^2 − 2x − 8 = (x − 4)(x + 2). Roots at x = −2 and x = 4. Because the parabola opens up, x^2 − 2x − 8 < 0 exactly on the interval (−2, 4) and > 0 for x < −2 or x > 4.

- x^2 + 2x − 8 = (x − 2)(x + 4). Roots at x = −4 and x = 2. It is < 0 on (−4, 2) and > 0 for x < −4 or x > 2.

So:
- If the graph shades the segment between −2 and 4, the answer is x^2 − 2x − 8 < 0.
- If it shades between −4 and 2, the answer is x^2 + 2x − 8 < 0.
- If it shades everything outside (−2,4), the answer is x^2 − 2x − 8 > 0.
- If it shades everything outside (−4,2), the answer is x^2 + 2x − 8 > 0.

Tell me which interval is shaded (or re-upload the image) and I’ll pick the correct choice.