Convert each of the following quadratic functions to vertex form by completing the

Question

square y=x^2+x+5

Answer 1

To convert the quadratic function y=x^2+x+5 to vertex form, we need to complete the square.

Step 1: Group the x terms together:
y=(x^2+x)+5

Step 2: Take half of the coefficient of the x term and square it. Add this value inside the parentheses, and subtract the same value outside the parentheses to keep the equation balanced:
y=(x^2+x+1/4)-1/4+5

Step 3: Rearrange the terms to have the squared term first, then group the constant terms together:
y=(x^2+x+1/4)-1/4+20/4

Step 4: Simplify the equation inside the parentheses:
y=(x+1/2)^2+19/4

So the quadratic function y=x^2+x+5 in vertex form is y=(x+1/2)^2+19/4.