Use the quadratic equation y=x^2+x+5 turn into vertex form

Answer 1

To turn the quadratic equation y=x^2+x+5 into vertex form, we can complete the square.

First, let's rewrite the equation as y = (x^2 + x) + 5.

To complete the square for the x terms, we need to add and subtract (1/2)^2 = 1/4 inside the parentheses:

y = (x^2 + x + 1/4 - 1/4) + 5

Now, let's rewrite the equation by grouping the perfect square terms together:

y = (x^2 + x + 1/4) - 1/4 + 5

Next, let's combine the constant terms:

y = (x^2 + x + 1/4) + 19/4

Since (x^2 + x + 1/4) is a perfect square trinomial, we can rewrite it as (x + 1/2)^2:

y = (x + 1/2)^2 + 19/4

Now, the equation y = (x + 1/2)^2 + 19/4 is in vertex form. The vertex form of the quadratic equation y = x^2 + x + 5 is y = (x + 1/2)^2 + 19/4.