### Video Transcript

What is the function whose graph is shown below?

To solve this question, weβre going to use the vertex form for the equation of a parabola. Vertex form says: π of π₯ equals a times π₯ minus β squared plus π, where β, π is the minimum or maximum for that parabola.

We have a very clearly defined β and π. Our β-value would be the π₯-value of the minimum, and it said negative six. Our π-value where the height of the minimum is zero. Letβs take the β and the π that we know and plug it into this vertex form.

We donβt know what a is, so weβll just leave the a there. Then weβll say π₯ minus our β, which is negative six. Now this is really important. The β-value in vertex form is being subtracted from π₯, and our β-value has a negative. So we need it to say π₯ minus negative six. And then we can square that value and add π, which is zero.

Now we wanna ask some questions about what our a-value does in vertex form. Hereβs what we know. When a is greater than zero, our parabola will open up. When a is positive, our graph opens upward. When a is negative, when a is less than zero, our graph will open downward. Since our graph is opening upward, we would say that our a is a one value; itβs positive. Then we can simplify a little bit and change π₯ minus negative six to π₯ plus six. And we can leave off that zero since its no value since our π-value is zero.

The parabola graph to the left can be represented by π of π₯ equals π₯ plus six squared.