question\nwhich equation best matches the graph shown below?\nanswer attempt 1 out of 2\n$\\circ\\ y = 2(x…

question\nwhich equation best matches the graph shown below?\nanswer attempt 1 out of 2\n$\\circ\\ y = 2(x - 2)^2 + 5$ $\\circ\\ y = 2(x + 2)^2 - 5$\n$\\circ\\ y = 2(x + 2)^2 + 5$ $\\circ\\ y = 2(x - 2)^2 - 5$
Answer
Answer:
$y=2(x+2)^2 + 5$
Explanation:
Step1: Recall vertex form
The vertex form of a quadratic function is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex.
Step2: Identify vertex from graph
The vertex of the parabola is $(-2, 5)$, so $h=-2$, $k=5$.
Step3: Substitute vertex into form
Substitute $h=-2$, $k=5$ into the vertex form: $y=a(x-(-2))^2+5 = a(x+2)^2+5$.
Step4: Confirm stretch factor
The parabola opens upwards and has a vertical stretch; the only matching option with this vertex is $y=2(x+2)^2 + 5$.