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.