ENG MS 465 Lecture Notes - Lecture 5: Completing The Square, Nth Root, Negative Number

• School: Boston University
• Department: Materials Science & Engineering
• Course: ENG MS 465
• Professor: Tsay- Vogel

Document Summary

: when a quadratic function is given in the vertex form, the parent function undergoes the following transformations. The function reflects over the x-axis if a is negative. The graph stretches or compresses by a factor of . If h is positive, (x (h)), it shifts right. If h is negative, (x (-h)), it shifts left. The vertex of the parabola is at coordinates (h, k: quadratic functions in vertex form (by completing the square) General form: f(x) = ax2 + bx + c f(x) = 3x2 12x + 7: factor out a from the first two terms. = 3(x2 4x) + 7: complete the square. = 3(x2 4x + 4) + 7 12: balance the equation f(x) = 3(x 2)2 5, factor and simplify vertex form. **you can only take the root of a negative number if the index is odd** **we can only multiply and divide radicals with the same index**