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What is the vertex form of the equation?
y=–x2+12x–4
To find the vertex form of the equation y = -x^2 + 12x - 4, we need to complete the square.
Step 1: Group the first two terms together and leave a space for completing the square:
y = -(x^2 - 12x) - 4
Step 2: Complete the square inside the parentheses. To do this, take half of the coefficient of the x-term (which is 12) and square it:
y = -(x^2 - 12x + 36) - 4 - (-36)
Step 3: Simplify:
y = -(x^2 - 12x + 36) + 32
Step 4: Write the x-term as a perfect square binomial:
y = -(x - 6)^2 + 32
Therefore, the vertex form of the equation y = -x^2 + 12x - 4 is y = -(x - 6)^2 + 32.