Video: Determining a Quadratic Equation in Standard Form from its Graph

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

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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 𝑓 of π‘₯ equals π‘Ž times π‘₯ minus β„Ž squared plus π‘˜, where β„Ž, 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„Ž equals six, and π‘˜ equals three. Instead of 𝑓 of π‘₯, we’ll use the variable 𝑦. We’ll say 𝑦 equals. We don’t know what π‘Ž is. But we can replace the β„Ž 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‘Ž, we’ll substitute negative one or, more simply, just a negative sign.

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

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