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The range of the quadratic function is the set of all real numbers and also the domain of the function is also set of all real numbers.
To find the range of the quadratic function f(x) = -2(x+3)² - 5, we need to consider the values that f(x) can take for all possible values of x in the domain of the function. The domain of a function is the set of all possible values of the input (x) for which the function is defined. For this function, the domain is all real numbers, because the function is defined for all values of x.
To find the range, we can start by finding the value of f(x) for specific values of x, or we can rewrite the function in standard form, which is f(x) = ax² + bx + c, where a, b, and c are constants. In this case, we can rewrite the function as f(x) = -2x² - 6x - 5.
Now we can use the range of a quadratic function formula to find the range: the range is all real numbers except for those that make the discriminant (b² - 4ac) negative. In this case, the discriminant is (-6)² - 4(-2)(-5) = 36 + 40 = 76, which is positive. Therefore, the range of this quadratic function is all real numbers. To summarize, the range of the quadratic function f(x) = -2(x+3)² - 5 is all real numbers, and the domain is all real numbers. If you want to use a domain and range calculator or a quadratic function calculator to find the range of this function, you can simply enter the function and the calculator will return the range and domain for you.
Learn more about Quadratic function at:
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