Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the vertex form of the equation? y=−x2+6x−7 (3 points)

Answer 1

To find the vertex form of the equation, y = -x^2 + 6x - 7, we need to complete the square. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex.

Step 1: Let's start by rearranging the equation to group the x-terms together: y = -(x^2 - 6x) - 7.

Step 2: To complete the square, we need to take half of the coefficient of the x-term (-6) and square it. Half of -6 is -3, and (-3)^2 = 9. So, we add 9 inside the parentheses: y = -(x^2 - 6x + 9 - 9) - 7.

Step 3: The expression inside the parentheses can now be written as a perfect square: y = -[(x - 3)^2 - 9] - 7.

Step 4: Distribute the negative sign: y = -(x - 3)^2 + 9 - 7.

Step 5: Simplify: y = -(x - 3)^2 + 2.

Therefore, the vertex form of the equation y = -x^2 + 6x - 7 is y = -(x - 3)^2 + 2. The vertex is located at the point (3, 2).