# Rewrite an equation in vertex form

Simplify some more, as necessary.

## Quadratic to vertex form calculator

Well, this is going to be equal to positive 20 over 10, which is equal to 2. Think of it this way : A positive "a" draws a smiley, and a negative "a" draws a frowny. And I am curious about the vertex of this parabola. The vertex is 2, negative 5. And the negative b, you're just talking about the coefficient, or b is the coefficient on the first degree term, is on the coefficient on the x term. This is the exact same thing that I did over here. So it's negative 20 over 2 times 5. This whole thing is going to hit a minimum value when this term is equal to 0 or when x equals 2.

I'll subtract 20 from the right hand side. Square the result, and add it to both sides inside the parentheses.

### Quadratic to vertex form calculator

I have equality here. This coordinate right over here is the point 2, negative 5. It's the x value that's halfway in between the roots. Or we could say it's always going to be greater than or equal to 0. 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. If you were to distribute this, you'll see that. Now it's not so satisfying just to plug and chug a formula like this. In the vertex form of the quadratic, the fact that h, k is the vertex makes sense if you think about it for a minute, and it's because the quantity "x — h" is squared, so its value is always zero or greater; being squared, it can never be negative. The sign on "a" tells you whether the quadratic opens up or opens down. So I have to do proper accounting here.

And we're going to do that by completing the square. So the x-coordinate of the vertex is just equal to negative b over 2a.

### Vertex form calculator wolfram

Simplify some more, as necessary. If I square it, that is going to be positive 4. I have equality here. And we talk about where that comes from in multiple videos, where the vertex of a parabola or the x-coordinate of the vertex of the parabola. And the highest point on a negative quadratic is of course the vertex. And then I have this 15 out here. Don't plan on using calculator cheats. 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 I have to do proper accounting here. And I am curious about the vertex of this parabola. If you take care to ensure that you have your quadratic completely converted to vertex form by being careful of the signs, then you'll be able to avoid one of the most commonly-made mistakes for these problems.

So I added 5 times 4. And I want to write this as a perfect square. And I am curious about the vertex of this parabola. I can't just willy nilly add a positive 4 here.

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