Find the domain and range for y= x^2 -6x -3 ?

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function is a quadratic function, which is defined for all real numbers. Therefore, the domain of y = x^2 - 6x - 3 is all real numbers.

The range of a function is the set of all possible output values (y-values) that the function can take. To find the range of a quadratic function, we can analyze the vertex of the parabola. The vertex of the parabola y = x^2 - 6x - 3 can be found using the formula x = -b/2a, where a = 1 and b = -6.

x = -(-6) / 2(1) = 6 / 2 = 3

Substitute x = 3 back into the original equation to find the corresponding y-value:

y = (3)^2 - 6(3) - 3
y = 9 - 18 - 3
y = -12

Therefore, the vertex of the parabola is (3, -12). Since the parabola opens upwards (a > 0), the range of the function is all real numbers greater than or equal to -12. In interval notation, the range is (-12, ∞).

Domain:

The domain of a function is the set of all possible input values (x-values). For the function y = x^2 - 6x - 3, there are no restrictions on the input value x. Therefore, the domain is all real numbers, represented as:

Domain: (-∞, ∞)

Range:

The range of a function is the set of all possible output values (y-values). To find the range, we need to determine the minimum and maximum values of y.

Step 1: Find the vertex

The vertex of a parabola is given by the point (h, k), where h = -b/2a and k = f(h). In this case, a = 1, b = -6, and c = -3:

```
h = -b/2a = -(-6)/2(1) = 3
k = f(h) = 3^2 - 6(3) - 3 = -12
```

Therefore, the vertex is (3, -12).

Step 2: Determine the direction of the parabola

Since a = 1 is positive, the parabola opens upward. This means that as x increases, y will also increase.

Step 3: Find the minimum and maximum values of y

Since the parabola opens upward and the vertex is (3, -12), the minimum value of y occurs at the vertex, which is y = -12. As x continues to increase, y will also continue to increase without bound. Therefore, the maximum value of y is ∞.

Range: [-12, ∞)

"I'm thrilled to share my incredible experience with Santoshi Hacker Organization! I had lost access to my Bitcoin wallet, and with it, a significant amount of cryptocurrency. I was devastated and thought all hope was lost. But then, I discovered Santoshi Hacker Organization, a team of expert hackers specializing in cryptocurrency recovery. I was skeptical at first, but their professionalism and expertise quickly put me at ease. The team at Santoshi Hacker Organization worked tirelessly to recover my lost Bitcoins. Their cutting-edge cybersecurity guide and black ATM expertise allowed them to navigate the complex web of blockchain transactions and successfully retrieve my funds. I was amazed when I saw my Bitcoins reappear in my wallet! The team's dedication, expertise, and discretion made the entire process seamless and stress-free. I wholeheartedly recommend Santoshi Hacker Organization to anyone facing similar challenges. Their exceptional service has restored my faith in the cybersecurity community. Thank you, Santoshi Hacker Organization, for your outstanding work!" Feel free to reachout to this Organization you we find help on your lost, Contacts: website :[ https://santoshi02.wixsite.com/santoshihackerfundsr } Email: { santoshihacker@hotmail.com }