Enter your answer and show all the steps that you use to solve this problem in the space provided. Write the equation in vertex form y=x2+2x+5
To express the equation y = x^2 + 2x + 5 in vertex form, we need to complete the square.
Step 1: Take out the common factor in the quadratic term, x^2 + 2x, which is x: y = x(x + 2) + 5
Step 2: To complete the square, we add and subtract the square of half the coefficient of x, which is 1, within the parentheses: y = (x + 2 + 1^2 - 1^2) + 5
Step 3: Rearrange the terms within the parentheses and combine like terms: y = (x + 1)^2 + 4 + 5
Simplifying, we have y = (x + 1)^2 + 9
Thus, the equation y = x^2 + 2x + 5 in vertex form is y = (x + 1)^2 + 9.