Question

Which quadratic function is represented by the graph?

y = 0.5(x + 2)2 + 4
y = 0.5(x + 3)2 – 0.5
y = 0.5(x – 3)2 – 0.5
y = 0.5(x – 2)2 + 4

Answer 1

I can’t see the graph — could you upload it or describe the vertex and one other point on the curve (for example the y‑intercept or an x‑intercept)?

Meanwhile, here’s how to choose from the four options quickly:

- All four open upward with a = 0.5 (wider parabola). So determine the vertex (h,k).
- Match the vertex to the form y = 0.5(x − h)^2 + k:
- y = 0.5(x + 2)^2 + 4 → vertex (−2, 4)
- y = 0.5(x + 3)^2 − 0.5 → vertex (−3, −0.5)
- y = 0.5(x − 3)^2 − 0.5 → vertex (3, −0.5)
- y = 0.5(x − 2)^2 + 4 → vertex (2, 4)

Pick the option whose vertex matches the graph. To be sure, plug a second plotted point (x0,y0) into the chosen equation; it should satisfy it.

If you post the graph or the vertex coordinates I’ll pick the correct equation for you.