If you’re looking for the equation of a graph with its vertex at the point (3, 2), you’re likely referring to a quadratic function, which can be expressed in vertex form. The vertex form of a quadratic equation is given by:
y = a(x – h)² + k
In this equation, (h, k) represents the vertex of the parabola. In your case, since the vertex is at (3, 2), we can substitute h with 3 and k with 2, which gives us:
y = a(x – 3)² + 2
Here, ‘a’ is a coefficient that determines the width and direction of the parabola. If ‘a’ is positive, the parabola opens upwards, and if ‘a’ is negative, it opens downwards. The larger the absolute value of ‘a’, the narrower the parabola.
For example, if we choose a = 1, the equation would be:
y = (x – 3)² + 2
This equation represents a parabola that opens upwards with its vertex located at the point (3, 2).
Feel free to experiment with different values of ‘a’ to visualize how they affect the graph!