Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Write down the coordinates of the minimum point of the curve:
[tex]\[ y = (x + 10)^2 + 4 \][/tex]

Sagot :

GinnyAnswer
To determine the coordinates of the minimum point of the curve [tex]\( y = (x + 10)^2 + 4 \)[/tex], we should analyze the structure of the equation. This given equation is in the form of a quadratic function in vertex form, which is typically expressed as [tex]\( y = a(x - h)^2 + k \)[/tex]. In this form, the vertex of the parabola, which represents the minimum or maximum point, is located at the coordinates [tex]\((h, k)\)[/tex].

For the quadratic function [tex]\( y = (x + 10)^2 + 4 \)[/tex]:

1. Identify the constants inside the equation:
- The term [tex]\((x + 10)^2\)[/tex] indicates that the horizontal shift is to the left by 10 units. By comparison with [tex]\((x - h)\)[/tex], we see that [tex]\( h = -10 \)[/tex].
- The constant term outside the square, [tex]\( + 4 \)[/tex], represents a vertical shift upwards by 4 units. This means [tex]\( k = 4 \)[/tex].

2. Combining these observations, the vertex (minimum point) of the quadratic function [tex]\( y = (x + 10)^2 + 4 \)[/tex] is at the coordinates [tex]\( (-10, 4) \)[/tex].

Thus, the coordinates of the minimum point of the curve are [tex]\( (-10, 4) \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.