What is the vertex form of the equation?y=–x2+12x–4
The vertex form of the equation is y = a(x-h)^2 + k.
To convert the given equation y = -x^2 + 12x - 4 into vertex form:
1. Complete the square for the x terms:
y = -(x^2 - 12x) - 4
y = -(x^2 - 12x + 36) + 36 - 4
y = -(x^2 - 12x + 36) + 32
2. Since (x - 6)^2 is equivalent to (x^2 - 12x + 36), the equation can be written as:
y = -(x - 6)^2 + 32
Thus, the vertex form of the equation is y = -(x - 6)^2 + 32.