### Video Transcript

Write the quadratic equation represented by the graph shown. Give your answer in vertex form.

We need to think about what a vertex form of a quadratic equation would be. We can represent the vertex form with the equation π of π₯ equals π times π₯ minus β squared plus π, where β, π is the vertex. The vertex is either the maximum or the minimum of your parabola. Our parabola opens downward. And that means we have a maximum at six, three.

The vertex of our graph is six, three. β equals six, and π equals three. Instead of π of π₯, weβll use the variable π¦. Weβll say π¦ equals. We donβt know what π is. But we can replace the β with six. And then we have π₯ minus six squared plus three, which is the π value.

Now, we know that this graph opens downward. And that means, in place of π, weβll substitute negative one or, more simply, just a negative sign.

The quadratic equation represented by this graph is π¦ equals negative π₯ minus six squared plus three.