Finding the Minimum Point by Completing the Square for y = x^2 - 10x + 9

Learn how to find the minimum coordinates of the quadratic curve y = x^2 - 10x + 9 by using the method of completing the square to rewrite the equation in vertex form.

Answer

To find the coordinates of the minimum point of the curve

by completing the square, follow these steps:

Step 1: Complete the square for the quadratic expression.
Take half of the coefficient of

(which is

), square it, and add and subtract it within the equation:
Half of

, and

Step 2: Identify the vertex (minimum point).
The equation is now in the vertex form

, where

is the vertex.
Comparing

to the vertex form:

Since the coefficient of

is positive, this vertex is the minimum point.

Final Answer:
The coordinates of the minimum point are

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