Question

Write the quadratic function f(x) = x2 - 5x + 3 in vertex form.

Answer 1

(x-5/2)^2-(25/4) +3
(x-5/2)^2-13/4

Vertex = (5/2, -13/4)

Answer 2

Finding the Vertex by "completeing the square"
Step 1. Insure the coefficient of the x^2 (the "a" term) is 1. In this case it is otherwise divide thru by the "non one" coefficient.

Step 2 Take the coefficient of the x term (b term) If the equations was modified to get the coefficient of the a term a one, use the modified coefficient of be, and divide by 2, (5/2) square this term (25/4) and add it to the equation. \[x ^{2}-5x +25/4 + 3\]
Since you added a value to the equation you must balance the equation by subtracting it:\[x ^{2}-5x + 25/4+3-25/4\]
Step 3. Thus far we have formed a "perfect square" with the \[(x ^{2}-5x+25/4)\] is a perfec square \[(x-5/2)^{2}\] Substitute the "squared" version getting:
\[(x-5/2)^{2}+3-25/4\]perform the addition and subtraction regroup the terms getting: \[f(x)=(x-5/2)^{2} - 13/4\] now in standard form. Now from the standard form it is apparent that the vertex occurs at the point (5/2, -13/4