To convert y = x² – 8x + 21 to vertex form, complete the square to get y = (x - 4)² + 5, where the vertex of the parabola is at (4, 5).
To convert the quadratic equation y = x² – 8x + 21 to vertex form, we complete the square. First, factor out the coefficient of x², which is '1' in this case, so no action is needed. We then focus on the x-terms. The equation can be rewritten as y = (x² – 8x) + 21.
To complete the square, take half of the coefficient of x, which is 4 (half of -8), and square it, resulting in 16. Add and subtract this number inside the parentheses: y = (x² – 8x + 16 – 16) + 21. Combining like terms, we get y = (x - 4)² + 5. This is now in vertex form, y = a(x - h)² + k, where (h, k) is the vertex of the parabola, and 'a' is the coefficient of the squared term in the original equation.
In our case, the vertex is at (4, 5) and the 'a' value remains '1' indicating the parabola opens upwards with a vertex at point (4, 5).