Write an equation in vertex form

Copy the original problem carefully.

Standard form to vertex form worksheet

And so the vertex here is x equals five, and I'm just gonna eyeball it, maybe it's right over here, x equals five. Notice this has been factored right over here. So if I take half of negative 4, that's negative 2. Y is equal to negative 27, so this right over here is negative The important thing to realize is that this part of the expression is never going to be negative. Well here, this is gonna be downward opening and let's appreciate why that is. This whole thing is going to hit a minimum value when this term is equal to 0 or when x equals 2. And what I'll do is out of these first two terms, I'll factor out a 5, because I want to complete a square here and I'm going to leave this 15 out to the right, because I'm going to have to manipulate that as well.

But another way to do it, and this probably will be of more lasting help for you in your life, because you might forget this formula. So now, you hopefully appreciate why this is called vertex form.

Write an equation in vertex form

Another common mistake is miscopying the original problem. Notice this has been factored right over here. So I'm going to do that right over here. Well here, this is gonna be downward opening and let's appreciate why that is. Well, it's going to be equal to zero when x plus two is going to be equal to zero. They are in different forms. Now it's not so satisfying just to plug and chug a formula like this. But another way to do it, and this probably will be of more lasting help for you in your life, because you might forget this formula. And so, x minus five is equal to zero. Copy the original problem carefully. It's a quadratic.

Because the coefficient on the x squared term here is positive, I know it's going to be an upward opening parabola. The vertex form tells you the vertex of the parabola, which way it opens, and whether it is a wide or narrow parabola. Well, this is going to be equal to positive 20 over 10, which is equal to 2.

Standard form of a quadratic equation

How do we do that? It's quite straightforward to pick out the vertex when you have something written in this way. Now, the reason why I was careful there is I didn't just add 4 to the right hand side of the equation. If you were to distribute this, you'll see that. So just like that, we're able to figure out the coordinate. So, where do we hit a maximum point? This is the first term.

And a is the coefficient on the x squared term. And you are able to pick that out just by looking at the quadratic in vertex form.

how to write a quadratic equation in vertex form with given points

Features of quadratic functions Video transcript I have an equation right here. So just like that, we're able to figure out the coordinate.

how to write an equation in vertex form from a graph
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Finding the vertex of a parabola in standard form (video)