Question

Convert each of the following quadratic functions to vertex form by completing the
square y=x^2+x+5

Answer 1

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

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

Step 2: Take half of the coefficient of x (which is 1) and square it.
(1/2)^2 = 1/4

Step 3: Add the value obtained in step 2 inside the parentheses and subtract it outside the parentheses.
y = (x^2 + x + 1/4 - 1/4) + 5

Step 4: Rearrange the terms inside the parentheses.
y = (x^2 + x + 1/4) - 1/4 + 5

Step 5: Simplify the equation.
y = (x + 1/2)^2 + 19/4

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