Answer:
The vertex form of the quadratic equation y = -x^2 + 12x - 4 is y = -(x - 6)^2 + 32, and the vertex is located at the coordinates (6, 32).
Explanation:
Step 1: Identify the coefficients:
The coefficient of x^2 is -1.
The coefficient of x is 12.
The constant term is -4.
Step 2: Complete the square:
Focus on the x terms and complete the square by taking half of the coefficient of x, which is 6, and squaring it, resulting in 36. Add and subtract 36 to the equation.
Step 3: Simplify the equation:
Simplify the equation by rearranging and simplifying the terms.
Step 4: Determine the vertex form:
The quadratic equation in vertex form is y = -(x - 6)^2 + 32, with the vertex at the coordinates (6, 32).