Finding Zeros with Technology Question © © Video Examples Find the zeros of the function \( f(x)=x^{2}-3 x-3 \). Round values to the nearest thousandths (if necessary). Answer Attempt 1 out of 2 \( \oplus \) Add a Zero \( \Theta \) No Zeros \( x=\square \) Submit Answer

To find the zeros of the function \( f(x) = x^2 - 3x - 3 \), we'll use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] For the given function: - \( a = 1 \) - \( b = -3 \) - \( c = -3 \) Plugging these values into the formula: \[ x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-3)}}{2(1)} = \frac{3 \pm \sqrt{9 + 12}}{2} = \frac{3 \pm \sqrt{21}}{2} \] Calculating the square root: \[ \sqrt{21} \approx 4.583666 \] Now, find the two solutions: \[ x_1 = \frac{3 + 4.583666}{2} \approx \frac{7.583666}{2} \approx 3.792 \] \[ x_2 = \frac{3 - 4.583666}{2} \approx \frac{-1.583666}{2} \approx -0.792 \] **Rounded to the nearest thousandth, the zeros of the function are:** \[ x = -0.792 \quad \text{and} \quad x = 3.792 \]