Let's first quickly review slope intercept form. Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope rate and the y-intercept. Continue reading for a couple of examples!
Transforming parabolas Video transcript - [Instructor] The function m is given in three equivalent forms. Which form most quickly reveals the y-intercept? So let's just remind ourselves.
If I have a function, the graph y is equal to m of x. And these are all equivalent forms, they tell us that. The function m is given in three equivalent forms.
I should be able to algebraically manipulate anyone of these to get any of the other ones. And so, if I wanted to graph y is equal to m of x, and let's say it looks something like this. I actually know it's a downward opening parabola, because I can look at this form right over here and say, "Hey look, the coefficient "on the second degree term here is a negative.
That's a messy drawing of it. And so if we're talking about the y intercept, we're saying, "Hey where does it intersect the y-axis? 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, I can substitute zero for x and so it'll be negative two times negative three times negative nine. So it's not too hard to figure out, but there's going to be some calculation in my head. Similarly in the second choice, for x equals zero, I then get negative six-squared, which is positive 36 times negative two, which is negative 72, and then I have to add that to positive I can do that, but it's a little bit of computation.
But here for this last one, and this is known as standard form, if I say x equals zero that term disappears, that term disappears and I'm just left with m of zero is equal to negative So standard form, this is standard form right over here, was by far the easiest.
So we know the y-intercept is zero comma negative Now one rule of caution.
Sometimes you might look at what is called, vertex form. And as we'll see this is the easiest one where it is to identify the vertex.
But when you see this little plus 18 hanging out, it looks a lot like this negative 54 that was hanging out. And you say, "Hey, when x equals zero, "maybe I can just cross that out "the same way that I cross these terms out.
When x is equal to zero, as I just said, you have negative six-squared, which is 36 times negative two. This is equal to negative So m of zero is definitely not So be very, very careful. But we can see that the best choice is this one, standard form, not vertex form or factored form.
Factored form, as you can imagine, is very good for figuring out the zeros. Let's do another example. And actually this is the same m of x, but we're going to ask something else. So it's given in those same three forms. Which form most quickly reveals the vertex?
Well I just called this 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 here is equal to zero.
Well, once you get used to vertex form, it'll just become a bit of second nature. But if this is a downward-opening parabola, the vertex is when you hit that maximum point.
And as you can see here, x minus six-squared is always going to be non-negative. You multiply that times the negative two, it's always going to be non-positive.
It's either going to be zero or a negative value, so this is always going to take away from this And so if you want to find the vertex, the maximum point here, it would be the x value that makes this thing equal to zero.
Because for any other x value, this thing is going to be negative, it's going to take away from that And so you can see by inspection, well what x value will make this equal to zero?How can you solve a quadratic function in intercept form?
How should it be written? Update Cancel. ad by ashio-midori.com How do you write a quadratic function in vertex form? Given a quadratic equation, how can I write another quadratic that intercepts the parabola only once?
We don't need to solve for the y-intercept, because it happens to be our vertex. Looking at the discriminant, we see that 0 2 – 4(-3)(1) = We have two real number roots, which means the function crosses the x -axis twice.
Next we will look at writing equations for quadratic functions. This is the form of a quadratic function. Quadratic functions are parabolas and either have a U-shape or a mountain shape.
Parabolas with a positive "a" value have a U-shape, and those . Sep 08, · How to Graph a Quadratic Equation When graphed, quadratic equations of the form ax 2 + bx + c or a(x - h) 2 + k give a smooth U-shaped or a reverse U-shaped curve called a parabola.
Graphing a quadratic equation is a matter of finding its vertex, direction, and, often, its x and y intercepts. Write a quadratic function for the parabola shown.
Solution Because you are given the x-intercepts p 1 and q 3, use the intercept form of the quadratic function. y a(x p)(x q) y a(x 1)(x 3) Use the other given point,(2, 3), to find a. 3 a(2 1)(2 3) Substitute for x and for .
Students will write zeros of a quadratic function in factored form. Graph a quadratic function in factored form. Identify maximum/minimum, axis of symmetry, vertex, zeros, .