Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. write the equation in vertex. y=x^2+2x+5
To write the given equation in vertex form, we can complete the square. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
Starting with the given equation y = x^2 + 2x + 5, we can complete the square as follows:
y = (x^2 + 2x) + 5
y = (x^2 + 2x + 1) + 5 - 1 (Add and subtract (1/2)^2 = 1 to maintain the equation's equality)
y = (x + 1)^2 + 4
Therefore, the equation y = x^2 + 2x + 5 can be written in vertex form as y = (x + 1)^2 + 4.