Question

which equation represents the curve shown on the graph?
the graph is a parabola opening upwards. the options are:
y = (x + 3)^2 + 2
y = (x - 2)^2 - 3
y = (x - 3)^2 + 2
y = (x + 2)^2 - 3

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Identify the vertex from the graph

From the given graph, the vertex (the minimum point of the parabola) is at \((2, -3)\). So, \( h = 2 \) and \( k = -3 \).

Step3: Substitute \( h \) and \( k \) into vertex form

Substituting \( h = 2 \) and \( k = -3 \) into \( y = a(x - h)^2 + k \), we get \( y=(x - 2)^2-3 \) (assuming \( a = 1 \), which is valid as the parabola opens upwards and has a standard shape).

Answer:

\( y=(x - 2)^2-3 \) (corresponding to the option: \( y=(x - 2)^2-3 \))