Answer:
y = -2(x - 1)² + 2
Explanation:
recall that the vertex form of a quadratic equation is :
y = a(x - h)² + k, where (h, k) is the coordinate of the vertex (i.e maxima point)
from the graph we can see that the vertex is at x = 1, y = 2
hence the answers that are valid would have h = 1 and k = 2
right away by observing the answers, we can see that the last 2 choices have h = (-1) and so these are NOT the answers.
To decide between the first 2 choices, we observe from the given graph, that when x=0, y=0.
The only choice which satisfies this is the 2nd option
Proof:
for y = -2(x - 1)² + 2, when x = 0,
y = -2(0 - 1)² + 2
y = -2(- 1)² + 2
y = -2(1) + 2 = -2 + 2 = 0 (Proven to be valid)
Sanity check: check the first choice
y = (x - 1)² + 2
when x = 0,
y = (0- 1)² + 2
y = 1 + 2 ≠ 0 (not the answer)