To convert the quadratic function y=x^2+x+5 to vertex form
To convert the quadratic function y = x^2 + x + 5 to vertex form, we need to complete the square.
Step 1: Rearrange the terms so that the x^2 and x terms are together.
y = (x^2 + x) + 5
Step 2: Add and subtract the square of half the coefficient of the x-term within the parentheses.
y = (x^2 + x + 1/4) - 1/4 + 5
Step 3: Group the first three terms and simplify.
y = (x^2 + x + 1/4) + 19/4
Step 4: Rewrite the first three terms as a square of a binomial.
y = (x + 1/2)^2 + 19/4
In vertex form, the quadratic function y = x^2 + x + 5 can be expressed as y = (x + 1/2)^2 + 19/4.