Determine the minimum value of y=(x-5)²

Recognize Quadratic Function: To find the minimum value of the function y=(x-5)², we need to recognize that this is a quadratic function in the form of y=a(x-h)²+k, where (h,k) is the vertex of the parabola. Since a is positive (a=1), the parabola opens upwards, and the vertex represents the minimum point of the function.Find Vertex Coordinates: The vertex of the parabola is given by the point (h,k). In the function y=(x-5)², h=5 and k=0, because the function can be rewritten as y=1*(x-5)²+0. Therefore, the vertex is at the point (5,0).Determine Minimum Value: Since the vertex (5,0) represents the lowest point on the graph of the function y=(x-5)², the minimum value of y is the y-coordinate of the vertex. Therefore, the minimum value of y is 0.

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Q. Determine the minimum value of

y=(x-5)^2

Recognize Quadratic Function: To find the minimum value of the function $y=(x-5)^2$ , we need to recognize that this is a quadratic function in the form of $y=a(x-h)^2+k$ , where $(h,k)$ is the vertex of the parabola. Since $a$ is positive ( $a=1$ ), the parabola opens upwards, and the vertex represents the minimum point of the function.
Find Vertex Coordinates: The vertex of the parabola is given by the point $(h,k)$ . In the function $y=(x-5)^2$ , $h=5$ and $k=0$ , because the function can be rewritten as $y=1*(x-5)^2+0$ . Therefore, the vertex is at the point $(5,0)$ .
Determine Minimum Value: Since the vertex $(5,0)$ represents the lowest point on the graph of the function $y=(x-5)^2$ , the minimum value of $y$ is the $y$ -coordinate of the vertex. Therefore, the minimum value of $y$ is $0$ .