Calculate Ascending Area of y=-(x+3)² : Quadratic Function Analysis

Question

Find the ascending area of the function

y=−(x+3)2 y=-(x+3)^2

Video Solution

Solution Steps

00:00 Find the domain of increase of the function
00:03 We'll use the formula for representing a parabola function
00:07 The formula for the intersection point with X-axis (P,K)
00:12 The member P equals (3)
00:16 The member K equals (0)
00:19 Intersection point with X-axis according to the members
00:22 We'll use abbreviated multiplication formulas to open the parentheses
00:25 Negative times positive always equals negative
00:28 Negative times negative always equals positive
00:31 We'll examine the coefficient of X squared, negative - concave function
00:35 The intersection point with X-axis is also the vertex point
00:41 In a maximum parabola, the domain of increase is before the vertex point
00:45 And this is the solution to the question

Step-by-Step Solution

We start by recognizing the function y=−(x+3)2 y = -(x+3)^2 , which is a parabola that opens downwards with its vertex at (−3,0) (-3, 0) . In the vertex form of a parabola y=a(x−h)2+k y = a(x - h)^2 + k , the values increase until reaching the vertex if the parabola opens downwards.

The expression y=−(x+3)2 y = -(x+3)^2 indicates that as x x moves towards −3-3 from the left, the function's values increase until reaching the vertex since the parabola is opening downwards.

Therefore, the interval over which the function is increasing corresponds to x<−3 x < -3 .

Thus, the ascending area of the parabola described by the function y=−(x+3)2 y = -(x+3)^2 is for x<−3 x < -3 .

Answer

x<-3

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