Find the Ascending Region of y=-(x-6)²: Quadratic Function Analysis

Video Solution

Solution Steps

00:00 Find the domain of increase of the function

00:03 Use the shortened multiplication formulas to open the parentheses

00:09 Negative times positive is always negative

00:14 Note the coefficient of X squared, negative - sad function

00:22 Examine the function's coefficients

00:27 Use the formula to find the vertex point

00:32 Substitute appropriate values and solve to find the vertex point

00:46 This is the X value at the vertex point

00:51 In a maximum parabola, the domain of increase is before the vertex point

00:57 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

The function given is $y = -(x-6)^2$ . This indicates that the parabola opens downwards because of the negative sign.

Step 1: Identify the vertex of the parabola:

The vertex form of a parabola is $y = a(x-h)^2 + k$ . Here, the vertex is at $(6, 0)$ .

Step 2: Determine the interval where the function is increasing:

Since the parabola opens downwards, the function is increasing as it approaches the vertex from the left.

Thus, the function is increasing for $x < 6$ .

Therefore, the correct answer is $x < 6$ .