Question

Which quadratic function is represented by the graph?

Answer 1

I can help — but I can't see the graph. Please either upload the image or tell me key points from the graph (vertex, intercepts, or three points on the curve).

While you get that to me, here are the common quick methods so you know what I'll do once you provide the info:

1. If you know the vertex (h,k) and one other point (x1,y1):
- Use vertex form f(x) = a(x−h)^2 + k.
- Solve a = (y1 − k) / (x1 − h)^2.
- Expand if you want standard form ax^2 + bx + c.

2. If you know the x-intercepts r1 and r2 (and one other point or y-intercept):
- Use factored form f(x) = a(x − r1)(x − r2).
- Solve a with the extra point (often the y-intercept at x=0).

3. If you know three points (x1,y1), (x2,y2), (x3,y3):
- Use general form f(x) = ax^2 + bx + c and solve the 3×3 linear system for a, b, c.
- Or use Lagrange interpolation / plug-and-chug elimination.

Example (vertex method): vertex (2, −3) and point (0,1)
- a = (1 − (−3)) / (0 − 2)^2 = 4/4 = 1
- f(x) = (x − 2)^2 − 3 = x^2 − 4x + 1

Send the graph or its key coordinates and I’ll find the exact quadratic.