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

00:06 Let's find where the function decreases.
00:11 First, use factoring formulas to expand the brackets.
00:17 Notice the coefficient of X squared is positive. This means it's a smiling function.
00:24 Next, observe the function's coefficients.
00:28 We'll use a formula to find the vertex point.
00:32 Substitute the right values into the formula and solve for the vertex point.
00:41 This gives us the X value at the vertex point.
00:47 In a parabola that opens upward, the function decreases before the vertex point.
00:56 And that's how we solve this problem!

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