We need a few points to graph this dude. The vertex and y and xintercepts are all relatively easy to find, so let's go with them. The vertex is at (3, 1). The yintercept is at x = 0, so plug that in. So, the yintercept is (0, 7). To find the xintercepts, if they exist, we need to multiply everything out. Just like Bigfoot or Australia, the xintercepts may not actually exist. Check the discriminant to see if they exist or not. The discriminant is negative, so Australia isn't real. And neither are the xintercepts for this function. We do need a few more points, though. We're going to show x = 1 and x = 4, but whatever you choose should work out the same. Collecting all of the points we've found into a table gives us the following. The last three points come from the function's symmetry, centered on the vertex. For instance, x = 6 is 3 away from the vertex, and so it shares a yvalue with (0, 7).
