The equation of a parabola with a vertex at the point (h, k) can be expressed in the vertex form:
y = a(x – h)² + k
In this case, our vertex is at (2, 0), meaning h = 2 and k = 0. Substituting these values into the vertex form gives us:
y = a(x – 2)² + 0
Simplifying this, we find:
y = a(x – 2)²
The value of ‘a’ determines the direction and width of the parabola:
- If a > 0, the parabola opens upwards.
- If a < 0, the parabola opens downwards.
- As |a| increases, the parabola becomes narrower; as |a| decreases, it becomes wider.
Without a specific value for ‘a’, we can represent the equation of the parabola simply as:
y = a(x – 2)²
To find a particular equation, you would need additional information, such as another point that lies on the parabola or the specific width or direction in which it opens.