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

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 𝑥 equals 𝑎 times 𝑥 minus ℎ squared plus 𝑘, where ℎ, 𝑘 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. ℎ equals six, and 𝑘 equals three. Instead of 𝑓 of 𝑥, we’ll use the variable 𝑦. We’ll say 𝑦 equals. We don’t know what 𝑎 is. But we can replace the ℎ with six. And then we have 𝑥 minus six squared plus three, which is the 𝑘 value.

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

The quadratic equation represented by this graph is 𝑦 equals negative 𝑥 minus six squared plus three.