This week, we learned all about graphing quadratic functions, doing this results in a Parabola. We can either graph from Vertex form or Standard form. First, let’s focus on graphing a function in Vertex form.

this is vertex form.

Let’s graph this function.

First, we should find the vertex. This is the most important point in a Parabola because from the vertex we can graph the rest of the parabola quickly and easily.

If we look at the function, it’s properties will tell us where the vertex is. the (x+4) in the function gives us horizontal movement, left or right.

Something you have to remember when graphing in Vertex form is that the horizontal movement will always be opposite to its value. For example, negative will move right, and positive will move left.

This is because to find the x-Intercept, has to equal 0. So, in this case, x would have to equal -4. Now, this is kinda complicated and honestly, it’s a lot easier to just remember it as the opposite movement (positive = negative and Vice Versa).

Now that we know the horizontal movement of the x-axis is -4. We only need to find the y-axis. This is simple, the final term in the function, +3, means we’ll move 3 vertically on the y-axis.

So, we know out vertex is 4 to the left, and 3 upwards. Giving us a vertex of -4, 3

Now we know the vertex, we can continue to graph the parabola. Because this function has a 2 in front, the parabola’s normal rate of change (1,3,5…) will be multiplied by 2 (2,6,10…)  

You can see by the graph that the rate of change is up 2, over 2, then up 6 over 2, and so on.

This is the basis for graphing a Quadratic function in Vertex form.