What is the vertex form of the equation?
y=-x^2+12x-4
y = -(x^2 - 12x) - 4
complete the square
y = -(x^2-12x+36) - 4 + 36
y = -(x-6)^2 + 32
To find the vertex form of the given equation y = -x^2 + 12x - 4, we can complete the square. The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Step 1: Group the x terms together.
y = -(x^2 - 12x) - 4
Step 2: Complete the square by adding and subtracting the square of half of the coefficient of x (in this case, 12/2 = 6).
y = -(x^2 - 12x + 36 - 36) - 4
Step 3: Rewrite the equation by grouping the squared term and the constant term separately.
y = -(x^2 - 12x + 36) + 36 - 4
Step 4: Simplify and rewrite the equation.
y = -(x - 6)^2 + 32
Thus, the vertex form of the given equation y = -x^2 + 12x - 4 is y = -(x - 6)^2 + 32. The vertex of this parabola is at the point (6, 32).