A parabola can be described by the standard form of its equation, which depends on its vertex. The vertex form of a parabola is given by the equation:
y = a(x – h)² + k
In this equation, (h, k) represents the vertex of the parabola. For a parabola with a vertex at (1, 2), we can substitute h = 1 and k = 2, resulting in:
y = a(x – 1)² + 2
Here, ‘a’ is a coefficient that determines the width and direction of the parabola (whether it opens upwards or downwards). Therefore, any equation that can be in the form of y = a(x – 1)² + 2 will satisfy the condition of having its vertex at (1, 2).
To summarize, look for an equation that fits this vertex form. If you have options, substitute the values into the vertex form and see which one matches.