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What is the domain of this quadratic function?\newliney=x2+2x−24y = x^2 + 2x - 24\newlineChoices:\newline(A){x∣x≥−25}\{x | x \geq -25\}\newline(B){x∣x≤−1}\{x | x \leq -1\}\newline(C){x∣x≥−1}\{x | x \geq -1\}\newline(D)all real numbers

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Q. What is the domain of this quadratic function?\newliney=x2+2x−24y = x^2 + 2x - 24\newlineChoices:\newline(A){x∣x≥−25}\{x | x \geq -25\}\newline(B){x∣x≤−1}\{x | x \leq -1\}\newline(C){x∣x≥−1}\{x | x \geq -1\}\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) for which the function is defined. 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. Confirming Quadratic Function Domain: To confirm the domain of the quadratic function y=x2+2x−24y = x^2 + 2x - 24, we need to check if there are any restrictions on the xx-values. Since there are no square roots, logarithms, or denominators that could potentially restrict the domain, we can conclude that the domain is all real numbers.
  3. Correct Choice Explanation: The correct choice that represents all real numbers from the given options is (D) all real numbers. This is because there are no xx-values that make the function undefined.

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