Features of quadratic functions Video transcript I have a function here defined as x squared minus 5x plus 6.
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.Find the x-intercepts (if any) for the graph of the quadratic function.
1.f(x) = (x + 2)2 - 4 Find the y-intercept for the graph of the math 11 4. a)how many different x-interceps could the graph of a quadratic function have? explain. it can have more than one because a parabola is a curved line on a graph in which case it touches two or more.
Key Learning: A quadratic equation can be written in standard form, vertex form, and intercept form. Each form provides different information needed for graphing the parabola.
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 . Practice Worksheet: Graphing Quadratic Functions in Vertex Form For # 1 -6, label the axis of symmetry, vertex, y intercept, and at least three more points on the graph.
Quadratic Equations make nice curves, like this one: Name The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x 2). Find Vertex and Intercepts of Quadratic Functions - Calculator: An applet to solve calculate the vertex and x and y intercepts of the graph of a quadratic function.
Match Quadratic Functions to Graphs. Excellent activity where quadratic functions are matched to graphs. graphing quadratic functions. quadratic functions (general form).