Calculate the Descending Area of y=(x-5)² in Quadratic Functions

Find the descending area of the function

$y=(x-5)^2$

Video Solution

Solution Steps

00:00 Find the domain of decrease of the function

00:03 Use shortened multiplication formulas for opening parentheses

00:09 Look at X² coefficient, positive - smiling function

00:15 Look at the function coefficients

00:20 Use the formula to find the vertex

00:25 Substitute appropriate values and solve to find the vertex

00:35 This is the X value at the vertex

00:41 In a maximum parabola, the domain of decrease is after the vertex

00:45 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will identify where the parabolic function $y = (x-5)^2$ is decreasing.

Step 1: Recognize the vertex of the parabola. The equation $y = (x-5)^2$ indicates the vertex is at $(5, 0)$ .
Step 2: Understand the direction of the parabola. This parabola opens upward as it is in the form $y = (x-p)^2$ .
Step 3: Determine the decreasing interval. For an upward-opening parabola, it decreases on the left side of the vertex.

From the vertex form of the parabola, we can conclude that the function decreases when $x < 5$ .

Therefore, the solution to the problem is $x < 5$ .