And in doing so, notice that this section down by the origin, we're going to round it off like this and then go up toward the right. Now we're going to connect the dots and assume that we have a general smooth shape between them. So again, kind of going up and about right there. When x was equal to negative 3, I ended up with 9. When x was equal to negative 2, I ended up with four. When I look at my negative values for x, when I went to x equals to negative 1, I ended up at 1. And lining it up, that looks about right. And then moving over three, we need to go up to 9. And then go over two units and go up to 2, 3, 4. Then moving over one unit and then up one unit, I have the 0.1 comma 1. So on the xy plane, let's just start at the origin of plot 00. Negative 1 squared is 1, 0 squared is 0, 1 squared is 1, 2 squared is 4, 3 squared is 9. Negative 2 times itself will end up giving us a value of 4. So negative 3 squared is the same as negative 3 times negative 3, which is going to give us a positive 9. So squaring all of our x values will give us our y-coordinates. Let's just plot values where x goes from negative 3 to positive 3 along integer values. In particular, if I just draw in a quick xy plane, and I'm going to just plot some points, so making a T-chart. We're going to do a little bit more detailed look at that graph now. Now, you may be familiar with this graph from having seen it in a previous section. So the most basic quadratic function is going to have the equation y equals x squared, or f of x equals x squared. We'll also look at methods for finding the vertex, and finally we'll look at optimization problems. We'll look at its intercepts and its vertex. We will consider the axis of symmetry for a quadratic function. We'll look at properties of a quadratic function, namely, we'll look at domain and range, and then we'll have the parabolic shape of the graph. In specifics, let's look at our subtopics. Now we're going to look at the two variable format where it's equal to f of x, a function of x. So just like we had looked at quadratic equations where we had ax squared plus bx plus c equals 0. A quadratic function is a function of the form f of x equals ax squared plus bx plus c, where a, b, and c are real numbers and our a value does not equal 0. Those are also known as second degree functions. We're now going to go up one degree and look at quadratic functions. Now, you should already be familiar with solving linear and quadratic equations, and in the previous session, we looked at linear functions.
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