Function Transformations and Translations

Students learn that if a quadratic equation is written in y – k = a(x – h)^2 form, the graph of the quadratic equation is a parabola with vertex (h, k). If the value of "a" is positive, the parabola opens upward, if the value of "a" is negative, the parabola opens downward, if the absolute value of "a" is greater than 1, the parabola is narrow, and if the absolute value of "a" is less than 1, the parabola is wide. For example, the parabola y + 6 = 5(x – 9)^2 has a vertex of (9, -6), opens upward, and is narrow.