Instructions: Given the function in standard form, use completing the square to write the function in vertex form and then identify the vertex.y=x2+2x+7
Question
Instructions: Given the function in standard form, use completing the square to write the function in vertex form and then identify the vertex.y=x2+2x+7
Solution
Step 1: Identify the coefficients from the standard form equation y = ax^2 + bx + c. In this case, a = 1, b = 2, and c = 7.
Step 2: Use the formula -b/2a to find the x-coordinate of the vertex. Here, -b/2a = -2/(2*1) = -1.
Step 3: Substitute x = -1 into the original equation to find the y-coordinate of the vertex. y = (-1)^2 + 2*(-1) + 7 = 1 - 2 + 7 = 6.
Step 4: Write the equation in vertex form, y = a(x-h)^2 + k, where (h, k) is the vertex. Here, the equation becomes y = 1*(x - (-1))^2 + 6, or y = (x + 1)^2 + 6.
So, the vertex form of the function is y = (x + 1)^2 + 6, and the vertex is (-1, 6).
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