Question

Which is the standard form of the equation of the parabola shown in the graph?

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Answer 1

I can’t see the images you attached. Could you either re-upload the graph image or describe the parabola (vertex, whether it opens up/down/left/right, and one other point on it or the x/y-intercepts)?

If you want to try on your own, here’s the quick method:

1. Identify the vertex (h,k) from the graph.
2. Determine the orientation:
- if it opens up or down use y = a(x − h)^2 + k
- if it opens left or right use x = a(y − k)^2 + h
3. Pick one other clear point (x1,y1) on the parabola and substitute into the chosen formula to solve for a:
- a = (y1 − k) / (x1 − h)^2 (for vertical parabolas)
- a = (x1 − h) / (y1 − k)^2 (for horizontal parabolas)
4. Write the final standard form with the found a, h, k.

Example: vertex (2, −1), opens up, passes through (3,1):
a = (1 − (−1)) / (3 − 2)^2 = 2 → equation y = 2(x − 2)^2 − 1.

Send the graph or its key coordinates and I’ll give the exact standard-form equation.