Convert each of the following quadratic functions to vertex form by completing the square y=^2+x+5
To convert the quadratic function y = x^2 + x + 5 to vertex form by completing the square, follow these steps:
Step 1: Group the x terms together.
y = (x^2 + x) + 5
Step 2: Complete the square by adding the square of half the coefficient of x to both sides of the equation.
In this case, the coefficient of x is 1, so half of it is 1/2.
Add (1/2)^2 = 1/4 to both sides.
y + 1/4 = (x^2 + x + 1/4) + 5
Step 3: Rewrite the trinomial as a perfect square.
y + 1/4 = (x + 1/2)^2 + 5
Step 4: Simplify and rewrite the equation in vertex form.
y + 1/4 = x^2 + x + 1/4 + 5
y + 1/4 = x^2 + x + 21/4
Finally, subtract 1/4 from both sides to isolate y, giving you the quadratic function in vertex form:
y = x^2 + x + 21/4 - 1/4
y = x^2 + x + 5.25
To convert the quadratic function y = x^2 + x + 5 to vertex form by completing the square, follow these steps:
Step 1: Group the x terms together.
y = (x^2 + x) + 5
Step 2: Take half of the coefficient of the x-term, square it, and add it inside the parentheses. Then, subtract the same amount outside the parentheses to maintain the equality.
y = (x^2 + x + 1/4) - 1/4 + 5
Step 3: Rearrange the expression inside the parentheses as a perfect square.
y = (x^2 + x + 1/4) + 19/4
Step 4: Simplify the square expression if possible.
y = (x + 1/2)^2 + 19/4
Therefore, the quadratic function y = x^2 + x + 5 can be written in vertex form as y = (x + 1/2)^2 + 19/4.