This evening, I'm continuing to review what I learned in this past summer's precalc course, and going over the introductions of some new concepts to prepare for the upcoming course.
A quadratic function's vertext form is "f(x) = a(x-p)² + q, where a, p, and q are constants and a ≠ 0" (Open School BC Pre-Calculus 11 Introduction Assignment). I practiced doing a couple of charts that gave me examples of quadratic equations and asked me to substitute in certain numbers for x and determine what the value of y was: for example, in the equation of y = -2(x-1)²+4, I needed to determine the value of y if x was 1, 0, 2, -1, 3, -2, and 4; in the equation y = 1/2(x+2)²-1, I needed to determine the value of y if x was -2, -1, -3, 0, -4, -5, 2, and -6. It was pretty straightforward, if a bit tedious; I just applied BEDMAS to the equations and rocked it. I then transferred those functions onto graphs. As I started to draw the graphs, I realized I'd made an error in my calculations: rather than flipping the polarity of the numbers due to the even-numbered exponent outside of the brackets, I'd treated them as I would have without the brackets, maintaining their positive or negative symbol. So I had to go back and redo the equations. Once I did, the graphs made sense again.