Question

Which quadratic function is represented by the graph?

f(x) = 0.5(x + 3)(x − 1)
f(x) = 0.5(x − 3)(x + 1)
f(x) = 2(x + 3)(x − 1)
f(x) = 2 (x − 3)(x + 1)

Answer 1

I don't see the graph — could you upload it or describe it (x-intercepts and one other point, e.g. the vertex or y-intercept)?

How to pick the correct one:
1. From the graph read the x-intercepts (the roots). That gives the factor pair:
- roots at x = −3 and x = 1 → factors (x + 3)(x − 1)
- roots at x = 3 and x = −1 → factors (x − 3)(x + 1)
2. Determine the vertical stretch factor k by using any other point (commonly the vertex or the y-intercept):
- if the other point is (x0, y0), then k = y0 / [(x0 − r1)(x0 − r2)].
3. Compare k to the choices (0.5 or 2).

Quick examples:
- If the x-intercepts are −3 and 1 and the vertex is at (−1, −2), then k = −2 / [ (−1+3)(−1−1) ] = −2 / (2·−2) = 0.5 → f(x) = 0.5(x + 3)(x − 1).
- If the x-intercepts are −3 and 1 and the vertex is at (−1, −8), then k = −8 / (2·−2) = 2 → f(x) = 2(x + 3)(x − 1).

Send the graph or its intercepts/vertex and I’ll pick the exact option.