#Factored form of a quadratic equation plus#

That looks like that, the roots are, or the In three equivalent forms, which form most quickly reveals the zeros or roots of the function? So once again, when we're talking about zeros or roots, if we have, let's say that's the x axis and if you have a parabola The vertex form and what is the vertex? Well it's going to happenĪt the point six comma 18. Of our two x-intercepts and then you could figure X-coordinate of the vertex is halfway between the x-coordinate Factored form you can find the zeros and then you'd know that the Standard form you couldĬomplete the square or do some other techniques or you could try to Happen at x is equal to six and then the y value there or the m of six is going to be equal to 18. So this lets us know very quickly that the vertex is going to Make this equal to zero? Well if x is equal to six, six minus six is equal to zero, zero-squared is zero, times negative two is zero. And so you can see by inspection, well what x value will

Because for any other x value, this thing is going to be negative, it's going to take away from that 18. And so if you want to find the vertex, the maximum point here, it would be the x value that Zero or a negative value, so this is always going

You multiply that times the negative two, it's always going to be non-positive. And as you can see here, x minus six-squared is always But if this is aĭownward-opening parabola, the vertex is when you Here is equal to zero.' How do I know that? Well, once you get used to vertex form, it'll just become a bit of second nature. Vertex form before, but what's valuable about the vertex form is you can really say, 'Okay, this is going to be, 'this is going to achieve its vertex 'when this thing over Reveals the vertex? Well I just called this And actually this is the same m of x, but we're going to ask something else. Factored form, as you can imagine, is very good for figuring out the zeros. But we can see that the best choice is this one, standard form, not vertex form or factored form. When x is equal to zero, as I just said, you have negative six-squared, which is 36 times negative two. And you say, 'Hey, when x equals zero, 'maybe I can just cross that out 'the same way that IĬross these terms out.' And be very, very careful there, because if x equals zero, this whole thing does not equal zero.

#Factored form of a quadratic equation plus#

Little plus 18 hanging out, it looks a lot like this negative 54 that was hanging out. And as we'll see this is the easiest one where it is to identify the vertex. Standard form right over here, was by far the easiest. I'm just left with m of zero is equal to negative 54. That term disappears, that term disappears and But here for this last one, and this is known as standard form, if I say x equals zero I can do that, but it's a little bit of computation. Get negative six-squared, which is positive 36 times negative two, which is negative 72, and then I have to add Similarly in the second choice, for x equals zero, I then So it's not too hard to figure out, but there's going to be When x is equal to zero? So it boils down to how quickly can we evaluate m of zero? What is m of x, when x is equal to zero? So how quickly can you evaluate m of zero? Well in this top one, IĬan substitute zero for x and so it'll be negative two times negative three times negative nine. It intersect the y-axis?' So what is the y value And so if we're talkingĪbout the y intercept, we're saying, 'Hey where does Term here is a negative.' So it's going to be aĭownward opening parabola. This form right over here and say, 'Hey look, the coefficient 'on the second degree I actually know it's aĭownward opening parabola, because I can look at Graph y is equal to m of x, and let's say it looks I should be able toĪlgebraically manipulate anyone of these to getĪny of the other ones. And these are all equivalentįorms, they tell us that. If I have a function, the graph y is equal to m of x. Reveals the y-intercept? So let's just remind ourselves. The function m is given in three equivalent forms.