To create an upside down parabola in vertex form, you need to understand the structure of the vertex form equation, which is typically written as:
y = a(x – h)² + k
In this equation:
- (h, k) represents the vertex of the parabola.
- a determines the direction and the width of the parabola.
For the parabola to open downwards, you must set a to a negative value. Here’s a step-by-step guide to formulating your upside down parabola:
- Choose the vertex: Decide on the coordinates of the vertex, (h, k). For instance, let’s say you want the vertex at (2, 3).
- Select a negative value for a: Choose a negative value for a that reflects the desired sharpness of the parabola. For example, let’s pick a = -1.
- Write the equation: Substitute the values into the vertex form equation. Plugging in our choices, we get:
y = -1(x – 2)² + 3
This equation describes an upside down parabola with the vertex at (2, 3). The negative coefficient before the squared term indicates that the parabola opens downward, and the vertex serves as the highest point of the graph.
To visualize this parabola, you can graph the function using a tool or coordinate plane, observing that it opens downwards from the vertex.