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What is the domain of this quadratic function?\newliney=x2−8x−20y = x^2 - 8x - 20\newlineChoices:\newline(A)x∣x≥−36{x | x \geq -36}\newline(B)x∣x≤4{x | x \leq 4}\newline(C)x∣x≥0{x | x \geq 0}\newline(D)all real numbers

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Q. What is the domain of this quadratic function?\newliney=x2−8x−20y = x^2 - 8x - 20\newlineChoices:\newline(A)x∣x≥−36{x | x \geq -36}\newline(B)x∣x≤4{x | x \leq 4}\newline(C)x∣x≥0{x | x \geq 0}\newline(D)all real numbers
  1. Function Domain Definition: The domain of a function refers to the set of all possible input values (xx-values) that the function can accept. For a quadratic function, which is a polynomial function, the domain is typically all real numbers because you can plug any real number into a quadratic equation and get a real number out.
  2. Check Quadratic Function: To confirm the domain of the quadratic function y=x2−8x−20y = x^2 - 8x - 20, we need to check if there are any restrictions on the xx-values. Since there are no square roots, logarithms, or any other operations that might restrict the domain in the given function, we can conclude that xx can take any real value.
  3. Confirm Domain Conclusion: Therefore, the domain of the function y=x2−8x−20y = x^2 - 8x - 20 is all real numbers, which corresponds to choice (DD) in the given options.

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