Functions, 2ADV EQ-Bank 09 Using the discriminant, or otherwise, justify why the graph of \(f(x)=-x^2+2 x-2\) lies entirely below the \(x\)-axis. (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only \(\Delta=b^2-4 a c=2^2-4(-1)(-2)=-4\) \(\text{Since \(\ \Delta<0, \ y=-x^2+2 x-2\ \) does not intersect the \(x\)-axis.}\) \(\text{Since \(\ a=-1<0, f(x)\) is an upside down parabola.}\) \(\Rightarrow f(x)\ \text{must lie entirely below} \ x\text{-axis.}\) Show Worked Solution \(\Delta=b^2-4 a c=2^2-4(-1)(-2)=-4\) \(\text{Since \(\ \Delta<0, \ y=-x^2+2 x-2\ \) does not intersect the \(x\)-axis.}\) \(\text{Since \(\ a=-1<0, f(x)\) is an upside down parabola.}\) \(\Rightarrow f(x)\ \text{must lie entirely below} \ x\text{-axis.}\)