# Rewriting a quadratic equation in vertex form

So that's one way to think about it.

So it is 5 times x squared minus 4x. So let's say let's pick a scenario where we have a downward opening parabola, where y is equal to, let's just say negative two times x plus five, actually, let me make it x minus five. And so this is never going to be negative and we're multiplying it by a positive right over here.

### Standard form of a quadratic equation

This whole thing right over here is going to be greater than or equal to zero. If you were to distribute this, you'll see that. Because the coefficient on the x squared term here is positive, I know it's going to be an upward opening parabola. Let me just rewrite it again. I don't know exactly where it intersects the x-axis but it's going to be a downward opening parabola. What is the vertex of the parabola here? Well, if x is equal to five and this thing is zero, you're not gonna be taking anything away from the 10 and so y is going to be equal to

Let me just rewrite it again. Features of quadratic functions Video transcript I have an equation right here. Well, to do that, we just have to appreciate the structure that's in this expression.

## Standard form to vertex form worksheet

This is the exact same thing that I did over here. I'm not using the same scales for the x and y-axis, but there you have it. I don't know exactly where it intersects the x-axis but it's going to be a downward opening parabola. So let's say let's pick a scenario where we have a downward opening parabola, where y is equal to, let's just say negative two times x plus five, actually, let me make it x minus five. You have your x-coordinate of the vertex right over there and you have your y-coordinate of the vertex right over here. Well here, this is gonna be downward opening and let's appreciate why that is. So let's say, I'm just gonna make this up, we have y is equal to negative pi times x minus 2.

So this whole thing right over here is going to be less than or equal to zero for all x's, so it could only take away from the It's a second degree equation. This is sometimes known as vertex form and we're not gonna focus on how do you get from one of these other forms to a vertex form in this video, we'll do that in future videos, but what we're going to do is appreciate why this is called vertex form.

The y value is going to be 5 times 2 squared minus 20 times 2 plus 15, which is equal to let's see. It's really just try to re-manipulate this equation so you can spot its minimum point. I have to be very careful here.

## Quadratic formula

Notice this has been factored right over here. The vertex is 2, negative 5. This is the first term. I could have literally, up here, said hey, I'm adding 20 and I'm subtracting So that's one way to think about it. You have your x-coordinate of the vertex right over there and you have your y-coordinate of the vertex right over here. So it's negative 20 over 2 times 5. Now, there's many ways to find a vertex. Exactly what's up here. It's a quadratic. And so, when will this equal zero? I have added 20 to the right hand side of the equation.

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