Questions: QUESTION 3 Given: f(x)=-3 x^2-x+2, find f(-1/2) 7/4 9/4 13/4 None of the above

Solution Steps

To find \( f\left(-\frac{1}{2}\right) \) for the function \( f(x) = -3x^2 - x + 2 \), substitute \( x = -\frac{1}{2} \) into the function and simplify the expression to find the value.

Given the function \( f(x) = -3x^2 - x + 2 \), we need to find \( f\left(-\frac{1}{2}\right) \). Substitute \( x = -\frac{1}{2} \) into the function:

\[ f\left(-\frac{1}{2}\right) = -3\left(-\frac{1}{2}\right)^2 - \left(-\frac{1}{2}\right) + 2 \]

Calculate each term separately:

1. \(-3\left(-\frac{1}{2}\right)^2 = -3 \times \frac{1}{4} = -\frac{3}{4}\)
2. \(-\left(-\frac{1}{2}\right) = \frac{1}{2}\)
3. The constant term is \(2\).

Combine these results:

\[ f\left(-\frac{1}{2}\right) = -\frac{3}{4} + \frac{1}{2} + 2 \]

Convert all terms to a common denominator and add them:

\[ f\left(-\frac{1}{2}\right) = -\frac{3}{4} + \frac{2}{4} + \frac{8}{4} = \frac{7}{4} \]

Final Answer