We need a few points to graph this function. The vertex and *y*- and *x*-intercepts are all relatively easy to find. The vertex is at (3, 1). The *y*-intercept is at *x* = 0. That is, So, the *y*-intercept is (0, 7). To find the *x*-intercepts, if they exist, we need to multiply everything out. *x*-intercepts may not actually exist, just like Big Foot or Australia. Check the discriminate to see if they exist or not.
The discriminate is negative, so Australia isn't real. And neither are the *x*-intercepts 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 on the *y*-axis, centered on the vertex. For instance *x* = 6 is three away from the vertex, and so it shares a *y* value with (0, 7). |