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Use \( g(x)=x^{2}-3 x+1 \) to find \( g(-3) \) \( g(-3)=19 \) \( g(-3)=1 \) \( g(-3)=-17 \) \( g(-3)=-3 x^{2}+9 x+1 \)

Ask by Howell Munoz. in the United States
Jan 22,2025

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\( g(-3) = 19 \)

Solución

To find \( g(-3) \) for the function \( g(x) = x^{2} - 3x + 1 \), substitute \( x = -3 \) into the equation: \[ g(-3) = (-3)^{2} - 3(-3) + 1 \] Calculate each term: 1. \( (-3)^{2} = 9 \) 2. \( -3(-3) = 9 \) 3. \( +1 \) remains the same. Now, add them together: \[ g(-3) = 9 + 9 + 1 = 19 \] **Therefore, \( g(-3) = 19 \).** Among the options provided: - \( g(-3)=19 \) ✅ - \( g(-3)=1 \) ❌ - \( g(-3)=-17 \) ❌ - \( g(-3)=-3x^{2}+9x+1 \) ❌ (This is not the value of \( g(-3) \), but rather an incorrect expression.) **Answer:** \( g(-3) = 19 \)

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Bonus Knowledge

To find \( g(-3) \), we simply substitute \(-3\) into the function \( g(x) = x^2 - 3x + 1 \). \[ g(-3) = (-3)^2 - 3(-3) + 1 \] \[ = 9 + 9 + 1 \] \[ = 19 \] So, \( g(-3) = 19 \) is the correct answer. As for the other options, \( g(-3) = 1 \) and \( g(-3) = -17 \) are incorrect as they do not match the output from our calculation. The last option, \( g(-3) = -3x^2 + 9x + 1 \), is simply a misrepresentation of the methodology for evaluating \( g \). Keep that calculator ready for the next math adventure!

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