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What is the domain of this quadratic function?\newliney=x2+12x+36y = x^2 + 12x + 36\newlineChoices:\newline(A){x∣x≤0}\{x | x \leq 0\}\newline(B){x∣x≥0}\{x | x \geq 0\}\newline(C){x∣x≥−6}\{x | x \geq -6\}\newline(D)all real numbers

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Q. What is the domain of this quadratic function?\newliney=x2+12x+36y = x^2 + 12x + 36\newlineChoices:\newline(A){x∣x≤0}\{x | x \leq 0\}\newline(B){x∣x≥0}\{x | x \geq 0\}\newline(C){x∣x≥−6}\{x | x \geq -6\}\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 any quadratic function in the form y=ax2+bx+cy = ax^2 + bx + c, where aa, bb, and cc are real numbers, the domain is always all real numbers because you can plug any real number into the function and get a real number out.
  2. Quadratic Function Example: To confirm this, we can look at the given quadratic function y=x2+12x+36y = x^2 + 12x + 36. There are no restrictions on the xx-values that can be substituted into the function. No matter what xx-value we choose, we will always get a real number for yy. This is true for all quadratic functions, which are defined for all real numbers.
  3. Domain of y=x2+12x+36y = x^2 + 12x + 36: Since there are no restrictions on the xx-values and the function is defined for all real numbers, the domain of the function y=x2+12x+36y = x^2 + 12x + 36 is all real numbers.

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