Calculate the Descending Area of y=(x+4)² : Step-by-Step Guide

Question

Find the descending area of the function

y=(x+4)2 y=(x+4)^2

Video Solution

Solution Steps

00:00 Find the domain of decrease of the function
00:03 Use the factoring formulas to expand the brackets
00:11 Note the coefficient of X squared, positive - smiling function
00:17 Observe the function's coefficients
00:21 Use the formula to find the vertex point
00:26 Substitute appropriate values and solve to find the vertex point
00:35 This is the X value at the vertex point
00:41 In a minimum parabola, the domain of decrease is before the vertex point
00:50 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will identify and use the vertex of the quadratic function. Knowing that the function y=(x+4)2 y = (x+4)^2 is a parabola, we recognize it is in vertex form. The general form of a parabola is y=(xh)2+k y = (x-h)^2 + k , hence the vertex of our function is at (h,k)=(4,0) (h, k) = (-4, 0) .

Next, it's important to understand the behavior of the function around this vertex. Since the parabola opens upwards (as can be seen from the positive coefficient of the squared term), it will decrease as x x moves towards negative infinity, reach its minimum value at the vertex, and then increase as x x becomes larger than the vertex.

Therefore, the function is decreasing on the interval to the left of the vertex. This describes when x<4 x < -4 .

To conclude, the solution to the problem is that the function is decreasing for x<4 x < -4 .

Answer

x < -4